Introduce yourself! · community: general

hello, I'm Christian. I'm studying with John Baez and the team at UC Riverside. I love category theory, and lots of things. currently I'm working for a distributed computing platform called RChain - it's based on a concurrent language, and we're using categories to give it a good type system.

James Fairbanks (Mar 23 2020 at 17:43):

Hi Christian, I’m James Fairbanks. I work on ACT for scientific modeling at Georgia Tech. We met at the AMS Riverside meeting.

Joe Moeller (Mar 23 2020 at 17:44):

Hi everyone! My name is Joe Moeller. I like using categories to study networks and combinatorics.

Bryan Bischof (Mar 23 2020 at 17:44):

I'm Bryan; I'm a mathematician working in Data Science/Algorithms for a tech company. In a previous life i did a Ph.D. in Noncommutative algebraic geometry and representations – very Categorical framing. I'm happy to learn connections between my new life and my old.

jpt4 (Mar 23 2020 at 17:46):

Greetings, my name is James Torre. I am interested in reconfigurable hardware and provably secure bootstrapping/modification of systems in general. Currently learning category theory avocationally so that I might better understand mathematical foundations and Conal Elliott's work on compiling categories to hardware.

Georgios Bakirtzis (Mar 23 2020 at 17:46):

:wave: I'm Giorgos. I apply category theory to systems theory at the University of Virginia, particularly in how to manage models of various flavours needed during the system design process.

Matt Cuffaro (he/him) (Mar 23 2020 at 17:47):

Matt Cuffaro (he/him) (Mar 23 2020 at 17:49):

I'm a software developer from Tampa, FL. I'm writing a paper on information geometry and another project on CT theory and Marxian economics

Johannes Drever (Mar 23 2020 at 17:57):

Hi, I’m Johannes, a software developer from Germany. I run an ACT learning group in Munich. I like functional programming and thinking about foundations of math. I want to apply category theory in data modeling and transformation.

philip hackney (Mar 23 2020 at 17:58):

David O’Sullivan (Mar 23 2020 at 17:58):

Hi all, I’m a lecturer at Sheffield Hallam Uni in the UK, background is Categorical Noncommutative Geometry (think *-categories enriched over Ban).

Robert Balicki (Mar 23 2020 at 18:03):

Hi, I'm Robert. I live in NYC. Interested in category theory, Rust, functional programming, etc etc. Check out www.smithy.rs. Employed software engineer.

John Vickers (Mar 23 2020 at 18:04):

I'm John Vickers. I did a Ph.D and PostDocs in Core Model Theory. I'm interested in Category Theory and Continental Philosophy and Poetry.

Caleb Foong (Mar 23 2020 at 18:05):

Hi I am data scientist from Malaysia. But I would think of myself just a mathematician that do a lot of programming. Been trying to categorizing all the thing ever since I met CT in undergraduate study.

Blake Pollard (Mar 23 2020 at 18:06):

Hi all, I'm Blake Pollard. I work on ACT at NIST where we are focused on CT as a meta-meta-modeling framework for systems, in particular model-based or model-driven design/systems engineering. Also interested in lots of other (some related) things: networks, data science, anywhere people draw pictures, formal methods, chemical reaction networks, information theory, complexity science, hyper-multi-inter disciplinarity.

philip hackney (Mar 23 2020 at 18:08):

philip hackney (Mar 23 2020 at 18:09):

Alpofblog (Mar 23 2020 at 18:10):

Hi I'm Alexandre. By day I'm a data scientist working on medical imaging, and whenever I have free time I work on math/music subjects, more specifically the formalization of musical structures using category theory.

Balaram Usov (Mar 23 2020 at 18:10):

:tada: I'm Balaram from Moscow. I have some mathematics background, but now I'm not at the academy. Most of the time, I’ve been doing activist projects where I could apply programming skills. Actually, last week I'm doing a bot for collecting user data on COVID19 pandemic in Russia. I also have some data analysis experience and now I'm learning TDA. I think that cool visualization can bring together different specialists to work on a common problem, as we see now with pandemic. TDA is also very interesting because it can help avoid research bias. There are interesting articles by Peter Bubenik, Nina Otter and other authors who use categories to develop the theory of persistent homology. But I also very interested in hardware/compilers, so the article mentioned by the @jpt4 intrigues me.

Evan Patterson (Mar 23 2020 at 18:13):

Hello! I'm Evan. I'm a PhD student in Statistics. I like category theory and applying it to statistics and other parts of applied math. I also build software for computational category theory.

Duncan Mortimer (Mar 23 2020 at 18:14):

Hi all! I'm Duncan. Like a few folk already, I'm a data scientist / ML engineer, currently working on an app to help people self-manage type 1 diabetes. In the past, I've done a PhD in computational neuroscience, and worked as an IT consultant. I've loved category theory from afar since my undergraduate days, and tried to get a grounding in it whenever I've had a spare moment. I'm really excited about the ACT movement! So much cool stuff going on :-)

Jules Hedges (Mar 23 2020 at 18:15):

Hi all. I'm Jules, a mathematician and theoretical computer scientist normally (but not right now) in Leipzig. My main interests are applying category theory to things like economics, optimisation theory and AI (broadly "cybernetics"), especially the theory and practice of graphical syntax

Paolo Perrone (Mar 23 2020 at 18:44):

Hey all! I'm Paolo, I work on category theory applied to probability and statistics, and I'm a passionate teacher too. I'm at MIT with David Spivak and Brendan Fong. I'm currently taking care of the online transition of many events, including the MIT category seminar and the ACT conference.
Thanks Jules for creating this!

Joe Moeller (Mar 23 2020 at 18:48):

Bartosz Milewski (Mar 23 2020 at 18:48):

Hi, I'm Bartosz. I popularize category theory, mostly to programmers (Haskell, and more recently, Scala as well). I like lenses and profunctor optics.

Joe Moeller (Mar 23 2020 at 18:48):

btw @Paolo Perrone, we were thinking it would be cool for this to be a place for both the MIT and UCR seminars to have conversations during talks.

Joe Moeller (Mar 23 2020 at 18:49):

Stelios Tsampas (Mar 23 2020 at 18:49):

Yoo, I'm Stelios, currently a CS PhD student in Belgium. Before that I was doing some shady computer security stuff. Right now I'm working on extending "mathematical operational semantics", a certain category-theoretic representation of PL. I find it amusing that this kind of work is foundational in PL theory yet applied in CT :P.

Paolo Perrone (Mar 23 2020 at 18:52):

Yep, I was thinking that too. Of course, that would require some testing beforehand. I'll ask the group today.

Christian Williams (Mar 23 2020 at 18:53):

John Connor (S2'16) (Mar 23 2020 at 18:56):

My name is John Connor. I am a Computer Science PhD student in NYC. I study type theory and logic, but I am interested in almost everything.

Stelios Tsampas (Mar 23 2020 at 18:58):

Ben Steffan (Mar 23 2020 at 18:58):

Hey, I'm Ben. I'm an undergrad in mathematics in Bonn. My interest in category theory is mostly in relation to algebraic topology.

Bartosz Milewski (Mar 23 2020 at 19:01):

I'm working with Brendan and David on finishing the notes. We'll publish them online when they are in a better state. They contain much more material than the lectures. There will be one more chapter after monads: profunctors, (co)end calculus, and optics.

Olga Lavinthal (Mar 23 2020 at 19:45):

hello. I am Olga, data scientist, statistician, and programmer. Learning category theory. :blush:

Philip Zucker (Mar 23 2020 at 19:54):

Hi, I'm Phil! I work at Draper Labs in the formal methods group. In a previous life, I did a PhD in the fractional quantum hall effect. I guess I'm most interested in concrete runnable implementations of categorical ideas.

John Baez (Mar 23 2020 at 19:54):

Hi, I'm John Baez. Lately I've been doing a lot of work on categories with open networks as morphisms with Brendan Fong, Daniel Cicala, Kenny Courser, @Joe Moeller and Jade Master. I've also been working with @Christian Williams on categories in computer science.

I think it's really great that we're starting this. Starting on Wednesday April 1st our group, ACT@UCR, will begin a series of online seminars at 10am Pacific time = 1pm East Coast time = 5pm (UTC+0). We hope all of you attend! We hope to have discussions afterward here!

janet singer (Mar 23 2020 at 19:57):

Hi all I’m janet, doing research in semiotics and GST (general theory of systems and cybernetics)

Stelios Tsampas (Mar 23 2020 at 20:02):

Christian Williams (Mar 23 2020 at 20:02):

Matt Cuffaro (he/him) (Mar 23 2020 at 20:05):

janet singer (Mar 23 2020 at 20:11):

The study of sign processes and relations: ‘Semiotics (also called semiotic studies) is the study of sign process (semiosis), which is any form of activity, conduct, or any process that involves signs, including the production of meaning.’ https://en.m.wikipedia.org/wiki/Semiotics

janet singer (Mar 23 2020 at 20:17):

Semiotics provides a great general framing for studying systems in terms of communication processes (biosemiosis, pansemiosis, etc.)

Emily Pillmore (Mar 23 2020 at 20:17):

Burak Emir (Mar 23 2020 at 20:18):

Hello, I am Burak. I left academia for industry after my PhD in programming languages ages ago, but continue to spend my spare time researching logics, types and categories. If I had to state a project involving categories, I'd say figuring out a practical query language for database. I regularly get lost in PL theory topics, too. These were at least three symbols of some sort, now :wink:

John Vickers (Mar 23 2020 at 20:21):

Why does Julia Kristeva use the word semiotic for the pre-infantile bodily process opposed to the symbolic? Can one model Kristeva in terms of the noncommutative topos or efforts to determine such?

John Baez (Mar 23 2020 at 20:24):

How are pre-infantile bodily processes related to "the noncommutative topos"? Actually I don't want to know that. What's "the noncommutative topos"?

Christian Williams (Mar 23 2020 at 20:24):

hey John, so this is an example where it would be great to start a stream, if enough people are interested. generally we're going to try to stay relevant to whatever "topic" we're in, though of course it's easy for conversation to diverge sometimes.

Asad Saeeduddin (Mar 23 2020 at 20:25):

Hello there. My name's Asad; I'm a programmer. Lately I've been obsessing over monoidal functors and strengths and how they model various patterns in day to day programming.

janet singer (Mar 23 2020 at 20:29):

A stream on semiosis/semiotics is a great idea. @John Vickers and @Matt Cuffaro which topic name would you prefer?

Reed Mullanix (Mar 23 2020 at 20:29):

Hey everyone! My name is Reed, and I'm a programmer with a background in Programming Languages Theory/Type Theory. I'm especially interested in the intersection of HoTT and (Higher) Category Theory.

Verity Scheel (Mar 23 2020 at 20:42):

Hi I'm Nick, I'm a cellist+math undergrad and I'm interested in HoTT/formalization/philosophy/functional programming but also want to learn more about vanilla category theory, since I still only know the basics.

janet singer (Mar 23 2020 at 20:42):

sarahzrf (Mar 23 2020 at 20:47):

sarahzrf (Mar 23 2020 at 20:48):

Christoph Horst (Mar 23 2020 at 20:48):

Hello, my name is Christoph. I once studied mathematics, nowadays I write C++, but I still love cats.

sarahzrf (Mar 23 2020 at 20:48):

Mike Stay (Mar 23 2020 at 20:52):

I was one of @John Baez 's grad students. I'm currently CTO of Pyrofex Corp. Right now I'm interested in formalizing the Casanova consensus algorithm, but I'm also talking with @Christian Williams about the semantics of concurrent programming languages.

sarahzrf (Mar 23 2020 at 20:54):

sarahzrf (Mar 23 2020 at 20:55):

Reed Mullanix (Mar 23 2020 at 20:59):

Matt Cuffaro (he/him) (Mar 23 2020 at 21:03):

Emily Pillmore (Mar 23 2020 at 21:03):

Philip Zucker (Mar 23 2020 at 21:07):

I am truly beyond flattered. Come for the @Emily Pillmore stay for the @Emily Pillmore

Nathaniel Virgo (Mar 23 2020 at 21:13):

Hi, I'm Nathaniel. I'm a complex systems scientist, currently teaching myself category theory and still very much a beginner. I'm interested in using it for information theory / probability theory, and maybe for trying to understand emergence.

Burak Emir (Mar 23 2020 at 21:13):

@janet singer a stream semio-* and production of meaning sounds pretty good. Are there known / already-articulated connections to CT?

John Vickers (Mar 23 2020 at 21:14):

I've not much time to give a reply tonight. I don't think Noncommutative Topos is an aporia and there was an attempt to define it last year. For Kristeva and the semiotic, in reply to @janet singer, one needs a womans body='place' or topos, which is minor in Deleuzes sense and radical or noncommutative, and whose internal logic is the feminine mysticism=Brouwerism. Another use might be in Topos Quantum Theory which is too bound to Kochen-Specker and the classical observation states. One might want something with stronger entanglement, using tensor products on Quantales. I'd like to have a Many World variant of (non)commutative Topos Quantum Theory. I'm not sure if you are doubtful of the use of a putative noncommutative Topos or you think its proper development could be valid only being more subtle than what I have in mind?

sarahzrf (Mar 23 2020 at 21:20):

John Baez (Mar 23 2020 at 21:23):

Sounds too vaguely formulated to me. People have tried inventing "quantum topos theory", but so far these attempts are miserable failures.

Christian Williams (Mar 23 2020 at 21:23):

@John Vickers, sorry can you please move this over to another topic? it's not part of people introducing themselves.

Thomas Read (Mar 23 2020 at 21:25):

Hi everyone! I'm a third year undergrad at Cambridge (UK), currently learning lots about algebraic theories (in particular Lawvere theories) in preparation for a summer research project

Burak Emir (Mar 23 2020 at 21:29):

@John Vickers @janet singer @Matt Cuffaro I created a stream called semiotics something.

John Vickers (Mar 23 2020 at 21:32):

I haven't got a clue how to use this software, moving or even putting something where I want it to be is beyond me at the moment.

Christian Williams (Mar 23 2020 at 21:33):

Burak Emir (Mar 23 2020 at 21:34):

Vlad Patryshev (Mar 23 2020 at 22:44):

Aaron Goodwin (Mar 23 2020 at 23:26):

Hi I'm Aaron. I'm a first year graduate student in math, interested in category theory. As to the conversation above, I would say that mysticism may be good for religious or spiritual purposes but it should really be kept separate from science.

Burak Emir (Mar 23 2020 at 23:34):

Mike Gallaher (Mar 24 2020 at 00:19):

Hi! I've been a software developer for several decades (a bit of everything), but my education was in EE (signal processing).
I still do electronics as a hobby, and amateur radio (WA2HEE).

I'm slowly working through Seven Sketches with a study group at work.
As I currently work at a data science company, I'm interested in functorial data migration, and the math behind linked data (RDF and such).
I thought Lisp had prepared me for functional programming, but Haskell showed me I have a lot to learn about CS math, not just CT.

As a learning exercise I'm trying to model software-defined radio flowgraphs. There's monoidal categories in there somewhere.

Jonathan Castello (Mar 24 2020 at 00:43):

Hi everyone! I’m a software developer with JPL; I work on multi-mission ground software at my day job, but in my spare time I like to study algebra, category theory, and logic programming languages. I’m particularly interested recently in applying the categorical mindset to reasoning about software architecture, as opposed to types or algorithms.

Right now I’m just working through Aluffi’s Algebra to warm up with a more familiar (undergraduate!) setting 😅

Ben (Mar 24 2020 at 00:49):

Hello, I'm Ben! I'm an undergraduate student in computer science with a very strong interest in Programming Language Theory and Category Theory. My current interest is in using CT to help in the software design process. Most papers I've found so far are above my level, so I'm going to catch up on a lot of reading once I'm finished with this last semester of school. I'm planning to start with Seven Sketches, if anyone would like to join me.

Ben (Mar 24 2020 at 00:51):

@Jonathan Castello Hey Jonathan! It sounds like our interests align. Would you be interested in studying with me?

Jonathan Castello (Mar 24 2020 at 01:03):

sarahzrf (Mar 24 2020 at 01:47):

@Jonathan Castello @Ben oh hey dont hesitate to ask me stuff, im extremely PL/programming ^.^

Faré (Mar 24 2020 at 01:57):

Hi! I'm François-René "Faré" Rideau, @ngnghm on twitter for computing stuff. I made trivial use of Category Theory in my unpublished PhD thesis to unify various computational paradigms and formalize the notion of Implementation of one with the other as (opposite of) profunctors, with natural transformations being opposites of code instrumentation / ornaments. At work, I am using both Game Theory and Game Semantics to model and implement applications that use blockchain smart contracts to keep the interests of participants aligned. And I'm hoping to also use Category Theory there. Yet I'm still a beginner who still doesn't fully grok the Yoneda Lemma.

John Baez (Mar 24 2020 at 01:57):

Faré (Mar 24 2020 at 01:57):

If you're in the Boston area or visit here, please come speak at the Applied Category Theory meetup.

Faré (Mar 24 2020 at 01:58):

Faré (Mar 24 2020 at 01:59):

My implementations are actually spans of a full embedding and a regular functor, plus many optional diagrammatic properties. I suppose I could relax the "full embedding" part to fit existing theories, but am not sure how to deal with the extra complexity then.

John Baez (Mar 24 2020 at 02:01):

Faré (Mar 24 2020 at 02:01):

Faré (Mar 24 2020 at 02:03):

Other questions I wonder: the relationship between a. the magic implicit lifting in most mathematical presentations of category theory (and in algebra in general) and b. quote and quasiquote and unquote in Lisp macros and c. hygienic macros that magically infer the level of quoting based on scoping.

Faré (Mar 24 2020 at 02:05):

^ point b. above is of course related to Guy Steele's speech on the semantics of vector notation in computer science papers, where he advocates for overbars and underbars that are related to Lisp Machine xapping and to quasiquoting in Lisp.

Faré (Mar 24 2020 at 02:12):

More questions: can we have a better more uniform notation for category theory and type theory, etc., where function types are covariant with function calls, so either prefix f(x) and a ← b, or postfix call x f and a → b but please no f(x) and a → b. And please no horrible mix of a→b bᵃ [a,b] a⇒b C[a,b] Mor(a,b) Hom(a,b) and more.

Ben (Mar 24 2020 at 02:13):

Emily Pillmore (Mar 24 2020 at 02:58):

Faré (Mar 24 2020 at 03:07):

Vinay Madhusudanan (Mar 24 2020 at 03:38):

Hello, everyone! I'm a mathematics teacher and researcher, currently working on my PhD in algebraic graph theory. I've been trying to study category theory. Right now my friend and I are working our way through Milewski's Category Theory for Programmers.

Vinay Madhusudanan (Mar 24 2020 at 03:42):

Also been reading Fong & Spivak's Applied Category Theory and giving text-only seminars on Telegram to a group of interested friends, but that's been going slowly (only because of my self-imposed seminar requirement).

John Baez (Mar 24 2020 at 04:02):

Joseph Dimos (Mar 24 2020 at 04:21):

Joseph Dimos (Mar 24 2020 at 04:36):

Some of my present involvements comprise the Chu construction and the realization of hypergraphs (in lieu of dialectica categories and DisCoCat) that attribute to Grinblat's case of endowing PetriNets with Zariski topology.

sarahzrf (Mar 24 2020 at 04:50):

Scott Morrison (Mar 24 2020 at 05:48):

I'm Scott Morrison, a mathematician interested in "low dimensional category theory", particularly with connections to topological phases of matter and quantum topology. I love 2- and 3- and even higher categories, but I mostly think about them from a very geometric point of view. If pressed, I will try to argue that (my corner of) higher category theory is more about manifolds, stratifications, cell-complexes, and geometric structures than it is about algebra or homotopy theory.

Mostly I work in the "fusion categories" or "quantum symmetries" community, where a lot of my work has consisted of connecting the sorts of categories which appear to describe topological phases in condensed matter physics with computational and classification problems.

I'm also one of the active contributors to the category theory library in Lean. mathlib (the mathematics library for Lean) is pretty amazing, growing faster, and rapidly approaching being useful. I'd be very happy to talk to people about this side of things, as well.

Jerry Swan (Mar 24 2020 at 07:39):

Firstly, thanks to Jules for kicking all this off and opening a window onto a wider world while we're all stuck indoors.

Most of my academic research has involved metaheuristic optimisation and/or program synthesis.
Nowadays, I'm working at NNAISENSE SA as an 'Artificial General Intelligence' researcher.

I'm particularly interested in category theory as a unifying principle in the design of intelligent systems (e.g. in the spirit of Goguen's later work).

Antonin Delpeuch (Mar 24 2020 at 08:45):

Hi everyone, I work on word problems with string diagrams, doing a DPhil in Oxford's Quantum Group. I am also quite excited about applied category theory and currently working on revamping OpenRefine's data model with CT in mind. On the side, I work with @Jules Hedges on bimonoidal categories at the moment. Thanks Jules for choosing Zulip! (it's FOSS, yay!)

Eigil Rischel (Mar 24 2020 at 09:06):

Hi all! I'm Eigil, an MSc student in Copenhagen. I'm working on the relationship between category theory and probability/statistics

Scott Morrison (Mar 24 2020 at 09:12):

Antonin Delpeuch (Mar 24 2020 at 09:17):

I do, he is my supervisor :) At the moment we are not working on a project together though - I am on a 1 year leave working full time on OpenRefine :)

Amar Hadzihasanovic (Mar 24 2020 at 10:10):

Hi, I'm currently a postdoc in Paris. I'm mainly interested in higher categories, diagrams, and rewriting, and connections to combinatorial topology and to proof theory.

Naso (Mar 24 2020 at 10:18):

Hi, I live in Brisbane Australia, I'm about to start a PhD at Uni of Qld researching verification of concurrent computer systems.

Ash Shevlyakov (Mar 24 2020 at 10:21):

Hi, i'm Andrey from Moscow, I work in control theory and robotics, on the lookout for something useful

Luc Chabassier (Mar 24 2020 at 10:30):

Hi ! I'm Luc Chabassier, studying computer science at the ENS of Paris. I am interested in logic, type theory, functional programming and category theory.

Anton Lorenzen (Mar 24 2020 at 10:56):

I am an undergrad mathematics student from Bonn working on type theory and formalization of mathematics in Lean. I have some experience with Haskell, Agda and @Bartosz Milewskis blog posts. If lectures get postponed further, I would be interested in forming a study group on Homotopy type theory and/or An Invitation to Applied Category Theory (whose authors are in this channel :)).

Anton Lorenzen (Mar 24 2020 at 10:57):

David Michael Roberts (Mar 24 2020 at 12:10):

Hi, I'm a mathematician in Adelaide, Australia. I work on what might be described as categorified geometry.

Fabrizio Genovese (Mar 24 2020 at 12:49):

Hello everyone, I'm Fab. I lead research at a company called Statebox where we apply CT to pretty much everything one can think of. Before that I did my PhD at Oxford with Bob Coecke about categorical quantum mechanics applied to language. Categorical Quantum Mechanics is very cool, while CQM applied to language is now the thing I hate the most in the whole ACT spectrum.

Fabrizio Genovese (Mar 24 2020 at 12:50):

Yo man! Long time no see! I didn't know you were into security but we should talk, we are really researching cryptography quite hard atm :)

Stelios Tsampas (Mar 24 2020 at 12:59):

Hey Fabrizio, awesome to see you here! I was wondering when you'd turn up :). Yeah, I used to be that guy haha. Vuln. research, exploit development, penetration testing and so on. We should absolutely talk, although crypto is not my strong suit :/.

Fabrizio Genovese (Mar 24 2020 at 13:01):

I'll create a cryptography substream in ACT later on today, and then we'll talk. :)

Stelios Tsampas (Mar 24 2020 at 13:02):

S. C. Steenkamp (Mar 24 2020 at 14:22):

Hi everyone, I'm a PhD student researching Type Theory and categorical semantics in the UK. Currently in my 2nd year.

Nicolas Blanco (Mar 24 2020 at 15:03):

Hello everyone and thanks to Jules and Christian for setting up this group!
I am a PhD student at the University of Birmingham (UK) with Noam Zeilberger and Paul Levy. My main areas of research are (linear) logic, (monoidal) category theory and their applications to (quantum) computer science. For my PhD, I am working on (bi)fibrations of polycategories and their relation to star-autonomous structures. Right now, I am working on a polycategorical Grothendieck construction that involves (the polycategory of) multivariable adjunctions.
In a former life, I was a software engineer using formal methods for developing safety-critical embedded software.

Yuri Ximenes Martins (Mar 24 2020 at 18:34):

Hello. I'm a PhD student at Federal University of Minas Gerais, Brazil. I work mostly on mathematical aspects of field theories (specially those involving (higher) categorical language and obstruction theory) and categorification. In my country category theory is not popular. Thus, I have no much people to talk and discuss. I helped to create a research group in my university, but we are always finding for some space (actually we have to fight even for very basic things). Thus, it is amazing for me to have this kind of contact! Thank you for this space. Really, thank you!!

Paolo Perrone (Mar 24 2020 at 18:41):

Aaaand, it's going to happen! The chat of the MIT Categories seminar will be right here :)

sarahzrf (Mar 24 2020 at 20:11):

Joe Moeller (Mar 24 2020 at 20:45):

John Baez (Mar 24 2020 at 20:50):

Jonathan Beardsley (Mar 24 2020 at 23:29):

Hello everyone, I'm Jonathan Beardsley. I'm a postdoc at Georgia Tech. I guess I technically do "homotopy theory," but I use a lot of category theory. Thanks to all who set this up. I think public spaces for talking about and learning math are wonderful.

Jonathan Beardsley (Mar 24 2020 at 23:33):

Probably should also say that my attendance here will likely be extremely spotty. We no longer have any childcare and I'm teaching from home and having to reorganize my entire 180 person differential equations class, so haven't had much chance to think about interesting math for a long time.

Florian Felix (Mar 24 2020 at 23:35):

Hello, I am Florian. I am a Graduate student in Münster, mostly interested in model theory and algebraic geometry and due to the latter (and a very nice seminar on logic in Topoi last semester) also in category theory :)

Ben Steffan (Mar 24 2020 at 23:35):

Fabrizio Genovese (Mar 24 2020 at 23:39):

My PhD thesis was on the application of CQM to Middle Egyptian (Hyeroglyphs). I don't agree with what you say, but maybe it's better to talk about this in private if you want to know more!

Bob Coecke (Mar 25 2020 at 00:03):

Oh dear, just learning Twitter and now this! I see my dearest academic kid Fabrizio is already giving a nice intro to CQM, and DisCoCat, or as he calls it CQM applied to language, which he hates more than anything; and which is some of the stuff I've done.

Joshua Tan (Mar 25 2020 at 00:03):

A new Slack! Long live the old Slack! Hello from Oxford, UK (temporarily Cambridge, MA in the time of corona). I'm Josh, I'm a PhD student at Oxford, where I do applied CT, theoretical ML, and... other stuff :-)

Joshua Tan (Mar 25 2020 at 00:04):

Also, the guy above me is one of my supervisors :grinning_face_with_smiling_eyes:

Ambroise (Mar 25 2020 at 00:04):

Hello! My name is Ambroise Lafont, I am a postdoc at UNSW in Sydney, working in the cogent team (https://ts.data61.csiro.au/projects/TS/cogent.pml). My PhD was about the specification of programming languages, eg the syntax is viewed as a monad on the category of Set.

Paul Blain Levy (Mar 25 2020 at 00:15):

Hi, I'm Paul Levy, programming language semantics is the centre of my world, but it spreads out in many directions, which tend to be categorical.

Paul Blain Levy (Mar 25 2020 at 00:23):

Paul Blain Levy (Mar 25 2020 at 00:24):

That was supposed to be a reply to Fare's introduction, but it's come out at the bottom of the thread.

Nathanael Arkor (Mar 25 2020 at 00:24):

to reply to a specific message, you can "Quote and reply" from the context menu on the message

Nathanael Arkor (Mar 25 2020 at 00:25):

Ohad Kammar (Mar 25 2020 at 00:25):

@Paul Blain Levy , you can think of streams as automatically defined filters for the stream of messages

Ohad Kammar (Mar 25 2020 at 00:25):

Paul Blain Levy (Mar 25 2020 at 00:25):

Paul Blain Levy (Mar 25 2020 at 00:26):

Paul Blain Levy (Mar 25 2020 at 00:27):

Paul Blain Levy (Mar 25 2020 at 00:28):

Jonathan Beardsley (Mar 25 2020 at 00:29):

I think "streams" and "topics" help with avoiding it becoming just a straight stream of consciousness

Ohad Kammar (Mar 25 2020 at 00:31):

Paul Blain Levy (Mar 25 2020 at 00:33):

Serdar Erbatur (Mar 25 2020 at 00:34):

Hi, this is Serdar Erbatur. My background is on unification theory, which is a subfield of automated reasoning and has connections to logic, algebra, category theory and TCS in general. I have also done a lot of research in PL (type-based program analysis) when I was postdoc in Germany (with Martin Hofmann between 2014 and 2018). I finished my PhD in 2012 and my advisor was Paliath Narendran. I had the privilage of collaborating with great people such Deepak Kapur, Jose Meseguer, Cathy Meadows, Christophe Ringeissen and many others. Currently, I am a teaching faculty at UT Dallas and continue my reseach. Before Dallas, I was a postdoc in three countries: one year in Italy, 3 years in Germany and approx one year in Spain. My research topics are quite theoretical, though I haven't applied anything from category theory myself. I know that a few category theoretic treatments were developed for unification in the past. I would be glad to talk about possible collaboration with anyone who have interest in my topics.

Chris Brown (Mar 25 2020 at 01:49):

Ben MacAdam (Mar 25 2020 at 01:59):

Hi everyone,
I'm Ben MacAdam, I'm a PhD candidate at the University of Calgary. I mostly work on tangent categories, and I'm particularly interested in how classical geometric structures such as Lie algebroids or linear connections can reappear as enriched Lawvere theories or enriched limit theories. I'm also interested in categorical axiomatizations of differential programming languages (which is where all of my actual publications have been so far).

Chris Brown (Mar 25 2020 at 02:00):

Ben MacAdam (Mar 25 2020 at 02:57):

Hi Rongmin, thanks yes. That also reminds me that I should spend some time tomorrow working on the nLab page.

Eduardo Ochs (Mar 25 2020 at 03:25):

Hi! My name is Eduardo Ochs, and I'm a mathematician working in a small countryside campus in Brazil. My papers, talks and notes are all here - <http://angg.twu.net/math-b.html> - and I've been working on something that I call "Categories for Children" (really - look at the URL above for the precise definition!). I'm currently working on 1) an obscure subproject of that that involves representing categorical concepts as diagrams, translating those diagrams to Type Theory, and applying a kind of projection that deletes all components that mention equalities of morphisms, 2) "Hyperdoctrines for children"...

Bryan Bischof (Mar 25 2020 at 04:32):

John Baez (Mar 25 2020 at 04:50):

Regarding tangent categorie: as far as I know, these are categories where each object is equipped with structure similar to the tangent bundle of a manifold. Cruttwell's talk Structures on tangent categories seems to be a gentle introduction.

Arjit Seth (Mar 25 2020 at 05:31):

Hello everynyan! I'm an MPhil student of aerospace engineering, but I'm also very interested in mathematics and physics. I'm studying Milewski's Category Theory for Programmers with @Vinay Madhusudanan.

Ryan Killea (Mar 25 2020 at 05:57):

Hi, I'm Ryan Killea, and I'm a software engineer. I'm interested quite broadly in ACT, but unfortunately have yet to actually use it in practice.

Alexander Kurz (Mar 25 2020 at 06:06):

Hi, I love category theory and everything related to logic and computer science ... looking forward to this forum.

David Michael Roberts (Mar 25 2020 at 06:36):

Sandro Pollastrini (Mar 25 2020 at 06:42):

Hi! I'm Sandro, a data-scientist from Italy with background in physics.
I fell in love with category theory when I read the Rosetta stone article of John.
Then I liked a lot the book of Milewsky and the one of Awodey.

My interest in category theory is twofold:
1 - a practical way to better organize my thoughts and my code when approaching the design of a program; also my work as a data-scientist implies to prove things as faster as you can sometimes (for business reasons): the better you are organized, the better and faster will be the results; and about the quality and repeatability of results, the functional programming point of view is very useful; I totally love the constructive mathematics potential
2 - having a unifying view over mathematics; I have the sensation that since I start understanding a bit of category theory, mathematics seems to me more as a unique thing, instead of a multiverse of different structures which sometimes happen to have connections ; this gave me also a different perspective over theoretical physics

Simon Pepin Lehalleur (Mar 25 2020 at 07:44):

Hi! I'm Simon Pepin Lehalleur. I am a postdoc in Nijmegen (Netherlands). I am interested in algebraic and arithmetic geometry, mostly through the angle of the many facets of the cohomology of algebraic varieties. My research focus is in the theory of motives and motivic homotopy theory. As such, I am mostly an end user of (higher) category theory, but I am always happy to learn more, and I am fascinated by the explosion of applied category theory.

Kenji Maillard (Mar 25 2020 at 07:55):

Hello everyone! I'm Kenji Maillard, a postdoc in Nantes (France) at Inria Galinette and University of Chile. I have been using CT for writing and specifying effectful (monadic) programs in dependent type theories.

Andrew Hirsch (Mar 25 2020 at 08:09):

Hi everyone! I'm Andrew Hirsch, a postdoc in Saarbrücken, Germany at MPI for Software Systems. My research focuses on giving a good foundation to security reasoning and enforcement. I've used CT theory largely to give semantics to effectful programs, but the more my research butts up against type theory, the more I find myself using it.

Martin Plávala (Mar 25 2020 at 08:13):

Hi all, I'm Martin Plávala, a postdoc in Siegen, Germany. Among other things I work on quantum foundations, specifically GPTs / convex theories, where tensor products / symmetric monoidal structures describe the composition rules of physical systems.

Isar Stubbe (Mar 25 2020 at 08:31):

Beppe Metere (Mar 25 2020 at 08:50):

Hi all. That's great! Thank you for setting this up! I am Beppe Metere, category theorist in Italy. I am a professor in Palermo University, but I am living in Milan. As you know, Milan is the epicentre of COVID19 infection in Europe, so that I am caged at home, with my family, and we do not know for how long. That's why I am very happy for all the seminars that are taking place online, and I hope to join you all there. Ciao! Beppe.

Jos Rozen (Mar 25 2020 at 08:57):

Hello. A scientist at Naver Labs Europe in Grenoble (France), I work on Natural Language Processing.

Fabrizio Genovese (Mar 25 2020 at 08:59):

I have no doubt things can be improved, the main problems I saw are the following:

Pierre Cagne (Mar 25 2020 at 09:07):

Hi everyone, I'm Pierre Cagne. I work in the field of categorical and homotopical algebra, and its relation to type theory. I'm currently in Bergen (Norway) working on homotopy type theory and group theory in univalent foudnations

Taichi Uemura (Mar 25 2020 at 09:48):

Chaitanya Leena Subramaniam (Mar 25 2020 at 09:53):

Hello everyone, I'm Chaitanya LS. I'm a PhD student in Paris, France, working on homotopy type theory and higher algebra. One of the things I'm currently interested in: It is possible to see type theories as "dependently sorted" Lawvere theories (aka contextual categories), and I'm trying to see if one can extract a good notion of "dependently coloured" operad from this.

Bob Coecke (Mar 25 2020 at 10:03):

@Fabrizio Genovese said something...reply:
On problem 1, there will be a paper soon on our recent implementation of DisCoCat on a quantum computer, where meanings are encoded in terms of variational learning.
On problem 2, in the first paper there was no such functor, and the real problem is that grammar and meaning are not independent, so no forward nor backward direction. On the other hand, grammar is no human invention, but a representation of stuff happening in the world out there.
On problem 3, this is now 100% settled as far as I am concerned, thanks to the evolving meanings in arXiv:1904.03478, with the meanings.

Lee Mondshein (Mar 25 2020 at 10:33):

Lee Mondshein (Mar 25 2020 at 10:34):

Matteo Capucci (he/him) (Mar 25 2020 at 10:35):

Click on a message, on the bottom of the page there's a textbox where you reply, the header of which allows you to select stream and topic

Lee Mondshein (Mar 25 2020 at 10:35):

Matteo Capucci (he/him) (Mar 25 2020 at 10:35):

Lee Mondshein (Mar 25 2020 at 10:35):

Fabrizio Genovese (Mar 25 2020 at 10:42):

Jonathan Beardsley (Mar 25 2020 at 12:01):

Paul Blain Levy (Mar 25 2020 at 12:03):

JS PL (he/him) (Mar 25 2020 at 12:03):

Hiya! I'm JS, a category theorist and finishing up my PhD at the University of Oxford. I work on all things "differential categories". Pretty cool that this chat was set up! Thanks!

Apoorv Ingle (Mar 25 2020 at 12:08):

Hi! Got here here from a twitter link. I am currently a CS PhD student at University of Kansas. My area of interests are Programming language semantics/Type systems. Great to see you all!

Juan Ferrer Meleiro (Mar 25 2020 at 12:18):

Hi! I'm a Mathematics PhD student at the University of São Paulo. I got here from the link at the n-Category Café. I have general interests in pretty much everything that's discussed here.

Paul Blain Levy (Mar 25 2020 at 12:21):

That was directed to David Roberts. Replying direct from email is not advisable, it would appear.

Yuri Ximenes Martins (Mar 25 2020 at 12:31):

Nathanael Arkor (Mar 25 2020 at 13:26):

@Fabrizio Genovese @Bob Coecke @Rongmin Lu: it would be better to continue this discussion in a separate thread — we should keep this one focused on introductions :)

Max New (Mar 25 2020 at 13:31):

Hi all, I'm a (final year) CS PhD student at Northeastern University working on programming language semantics heavily influenced by category theoretic approaches. On the application side my focus is on "gradual typing", interoperability between languages and low-level/intermediate languages, and on the category theory side my interests include categorical logic generally, and more specifically (virtual) double categories, generalized multicategories and gluing approaches to formalizing logical relations

Daniel Geisler (Mar 25 2020 at 13:56):

Hello, I'm Daniel, a software engineer with an interest in CT, dynamics and combinatorics. I'm a big fan of Flajolet's work in analytic combinatorics. I am also the author of http://tetration.org. I consider Stephen Wolfram a valued mentor and am working on upgrading my iterated function and hyperoperator Mathematica software for Wolfram Functions.

Question: Can an iteration functor map a category into the next higher category? Then I may be able to use what I've learned from studying the hyperoperators as a sequence of higher iterated functions to provide some insight into higher categories.

Alex Kavvos (Mar 25 2020 at 13:56):

Hi all. I'm a postdoc at Aarhus University. I'm interested in applications of category theory to the semantics of programming languages and type theories.

Nathanael Arkor (Mar 25 2020 at 14:10):

@Chaitanya Leena Subramaniam: I've spent some time thinking about the right notion of dependently-sorted multicategories as well; I'd be interested to discuss it with you (I've seen your slides on contextual categories as monoids, and had a couple of questions about that approach)

Chaitanya Leena Subramaniam (Mar 25 2020 at 15:17):

@Nathanael Arkor:
Yes, definitely! I see you're at Cambridge, so you are perhaps familiar with Fiore's "Second-Order and Dependently-Sorted Abstract Syntax". In fact, the definition of "type theory" in my slides is exactly the same as Fiore's "

\Sigma_0

-model with substitution" (We didn't know about this paper when coming up with our definition, which is why it's not mentioned in the talk. Marcelo Fiore pointed it out to me subsequently.)

Bob Atkey (Mar 25 2020 at 15:56):

Hello, I'm Bob Atkey. I'm a Computer Science lecturer at Strathclyde Univesity in Glasgow. I'm interested in category theory for semantics of linear dependent type theories.

Ohad Kammar (Mar 25 2020 at 16:00):

Oscar Ponce (Mar 25 2020 at 16:31):

Hi all, I'm a software engineer with an interest in CT. I'm mainly interested in CT and functional programming applications.

Daniel Cicala (Mar 25 2020 at 16:46):

Hello. I'm Daniel Cicala, a lecturer at University of New Haven. I'm interested in CT perspectives on rewriting and network theory. Cool seeing so many familiar people here. Thanks for setting this up! (Christian, was it you?)

Max Wall (Mar 25 2020 at 17:23):

Hi all. I'm Max Wall, a software engineer at Moderna Therapeutics. I'm excited about applications of CT in data integration and probabilistic programming language semantics. I'm an amateur enthusiast, so this is very exciting to have a little window into the world of the pros. Thanks for the invite!

Refurio Anachro (Mar 25 2020 at 17:28):

Hi! Am amateur, occasional maths blogger, enthusiast, software architect and entrepreneur.

Refurio Anachro (Mar 25 2020 at 17:29):

Antonin Delpeuch (Mar 25 2020 at 17:30):

Bob Atkey (Mar 25 2020 at 17:40):

Gershom (Mar 25 2020 at 17:43):

I'm a computer scientist in industry who dabbles in category theory and co-organizes (when there isn't a pandemic) the ny category theory seminar. A high level summary of what I'm focusing on thinking about at the moment is "topological models of concurrency and nondeterminism".

Ben MacAdam (Mar 25 2020 at 17:55):

Hi Alexander - I believe we met at SYCO last summer. It's great to see you here, I've basically spent all year looking at some of those applications of Lawvere theories to SDG we discussed!

David Navia (Mar 25 2020 at 18:20):

Hello! My name is David Navia, I'm a physicist working on quantum foundations from a categorical perspective

Emily Riehl (Mar 25 2020 at 18:32):

Hi everyone. I'm a mathematician interested in higher category theory and homotopy type theory, normally based in Baltimore but currently stationed in Berkeley in hopes that MSRI will re-open before the end of May. I hope you all are holed up somewhere safe and relatively comfortable.

Timothy Porter (Mar 25 2020 at 19:00):

Hi there from North Wales. I'm a `retired' category theorist. (You may know that Bangor University shut its maths department in 2006) I am still active and am working on categorical problems relating to TQFTs and infinity categories.

David Jaz (Mar 25 2020 at 19:02):

Hi everyone! I'm one of Emily's students, interested in homotopy type theory, higher category theory, and what it means to be a thing. Hope you all are safe and well, wherever the pandemic has placed you.

Morgan Rogers (he/him) (Mar 25 2020 at 19:42):

Hi all! I'm one of Olivia Caramello's PhD students. I study topos theory, particularly Grothendieck toposes of monoid actions. Although we're normally based in Como in Italy, Olivia is stuck working from an apartment by the IHES in Paris, and I am working from home in the UK. I hope everyone has a comfortable space to live and work in through these times.

Brandon Shapiro (Mar 25 2020 at 20:01):

Hi! I'm a grad student working on higher category theory, broadly construed, as well as homotopy theory, applied category theory, and HoTT. I'm very interested in comparing how different types of cell shapes can be used in these areas, and how many different dishes I can cook before my brother agrees to eat one of them. Hope everyone stays safe!

Saul Hilsenrath (Mar 25 2020 at 20:12):

Hi, I'm a student at the University of Maryland interested in higher category theory, categorical logic, and homotopy type theory, and I'm working on the application of higher toposes to integrability. I'm a participant in the Applied Category Theory seminar at UMD, organized by Noah Chrein, and I'm a member of a subgroup of the seminar participants working on compositional machine learning.

Rich Hilliard (Mar 25 2020 at 20:13):

Hi! I work on systems and software architecture, both research and practices; interested to apply categorical methods to that work for architecture description and specification.
Usually found in Bar Harbor, Maine US.
Stay safe!

David Egolf (Mar 25 2020 at 20:58):

Hi all! I'm an engineering grad student at University of Alberta. I'm interested in using category theory to think about medical imaging systems.

Ben MacAdam (Mar 25 2020 at 21:02):

Hi David - Jonathan Gallagher and I are at the University of Calgary (well, he's a visiting postdoctoral fellow) and we've been thinking about similar things!

Júlio Veloso Jr. (Mar 25 2020 at 21:22):

Hi! I'm undergrad math student at UFSC (Brazil). Today I study philosophical logic with a professor and stone duality with another. My (future) interests are foundations of math/science, operator algebras and a little of mathematical physics.

Carl Stuendel (Mar 25 2020 at 21:22):

Hi everyone! My interest is in philosophy. Regarding category theory, I'm still very much a novice though my first exposure to it was a passing reference in 1972. I come to this forum by way The n-Category Café.

Min Ro (Mar 25 2020 at 21:46):

Hello! I'm an instructor at the 2 year college University of New Mexico, Los Alamos. When I was a graduate student, I did stuff involving Cstar-algebras. While I'm not a research mathematician (anymore?), I am interested in the relationship between category theory and functional analysis, especially Banach spaces and C*-algebras and the like. Seeing how difficult it is for me to read through everyone's intros, I wonder if this will get lost in the shuffle.

Fatima Afzali (Mar 25 2020 at 22:14):

Hi! I'm a junior undergrad at Florida International University. I've spent this year studying higher/category theory and physics, and will spend the next studying applied category theory and related concepts.

Ambroise (Mar 25 2020 at 22:38):

(=_=) (Mar 26 2020 at 00:20):

Hi @Max Wall! Just curious as to what you're aware about applications of CT in these two areas. For data integration, did you have in mind the data migration of Spivak et al's FQL? For probabilistic programming language semantics, that's new to me, any pointers to the literature you've seen? Thanks!

Conor McBride (Mar 26 2020 at 00:29):

I'm Conor McBride when I'm being British, but I'm also Irish. I'm a dependently typed functional programmer with an increasingly categorical bent. In the past I have noticed a peculiar inability to learn category theory. Fortunately, I can be co-learned by category theory. It keeps showing up in the things that I'm doing, and I can't help thinking I could be doing them more deliberately.

(=_=) (Mar 26 2020 at 00:31):

Ralf Meyer has done a fair bit of work on this and is writing up a book on 2-categories in noncommutative geometry.

Min Ro (Mar 26 2020 at 00:45):

Oh, yes, I really need to read some of Ralf Meyer's work, especially since I was involved in Elliott's classification. His book on K-theory co-authored with Cuntz and Rosenberg has been on my to read list for way too long. The news of him writing a book on 2-categories is exciting!

(=_=) (Mar 26 2020 at 00:47):

He was looking for references for historical remarks for the manuscript late last year in a mailing list I subscribe to (thanks, @Emily Riehl, for sending him there), so perhaps he's still open to having more readers.

Todd Trimble (Mar 26 2020 at 02:53):

Hi, I'm Todd Trimble. Have recently returned to academe after a long hiatus, but some of you may know me from the n-Category Cafe, MathOverflow, and the nLab. Among other things, I enjoy thinking about how geometry and topology enter the study of free categorical structures.

Alex Kreitzberg (Mar 26 2020 at 04:00):

Hello, I'm Alex Kreitzberg. I'm a math teacher at the Prime Factor Math Circle. I'm interested in explorable explainations (https://explorabl.es/) and educational games. I enjoy Mathematical Physics. So I'd like to understand, if only partially, Category Theory's relationship with Logic, Probability, Analysis and Differential Geometry.

There are a lot of very good category theorists here, so I'll try not to be a bother.

Faez Shakil (Mar 26 2020 at 04:06):

Hi everyone! I’m Faez, I live in Pakistan and have spent the last 6 months trying to get Solar Microgrids to self-assemble with the power of cospans. I’ve developed the terrible habit of not asking any questions about things I don’t understand and am here in the hope that you all will be great for helping me break out of my onanistic habits.

nadia esquivel márquez (Mar 26 2020 at 05:49):

Hello there! I'm nadia, undergrad at the national autonomous university of mexico, interested in abstract homootpy theory (and everything that comes along with it)

T Murrills (Mar 26 2020 at 07:20):

Hi all! You can call me T! I'm at Rutgers working on a (hopefully) soon-to-be-complete undergraduate degree.

I'm interested in higher category theory, HoTT, and foundations of math (both philosophical and, well, mathematical). I also have a strong interest in designing computational proof representation and verification—and especially in doing so from the vantage point of my other mentioned interests!

Gordon Plotkin (Mar 26 2020 at 08:07):

Hi, I am Gordon Plotkin, interested in applications of category theory and logic more broadly to computer science. Great to see virtual life expanding in these difficult times, and many thanks to the organizers!

Robin Piedeleu (Mar 26 2020 at 08:10):

Hi everyone! I'm Robin, a postdoc at UCL who enjoys thinking about all sorts of graphical languages from a categorical perspective. My research is mostly in theoretical computer science with a broader focus on the study of open systems that pop up in different scientific contexts. I primarily employ algebraic tools, with an emphasis on monoidal (higher) categories and diagrammatic reasoning as a unifying language. Thanks to whomever started this group! I hope you're all safe in these troubled times.

David Michael Roberts (Mar 26 2020 at 09:01):

Hi again, this time with a different hat on. I'm also interested in (pre)topos-theoretic approaches to foundations, specifically the problem of how to do class forcing with categories, and independence proofs of a large structural nature.

Christina Vasilakopoulou (Mar 26 2020 at 09:58):

Hi! I'm Christina Vasilakopoulou, currently a researcher at the University of Patras, Greece. Interested in all sorts of category theory :)

Chad Nester (Mar 26 2020 at 10:04):

Enric Cosme Llópez (Mar 26 2020 at 10:43):

Hi! I’m Enric Cosme, a researcher at the Universitat de València in Spain. I’m here to learn from all of you. Thanks for starting this!

Paolo Capriotti (Mar 26 2020 at 11:42):

Hi all, I'm a postdoc at TU Darmstadt, working on homotopy type theory and higher categories.

Jonathan Beardsley (Mar 26 2020 at 12:13):

@nadia esquivel márquez
```` Hello there! I'm nadia, undergrad at the national autonomous university of mexico, interested in abstract homootpy theory (and everything that comes along with it)''''

Hi Nadia, I made a topic in #category theory called "homotopical category theory," so if you wanna chat about homotopy theory stuff, feel free to post in there or anywhere else!

Jonathan Beardsley (Mar 26 2020 at 12:13):

Dr. Peter Nonnenmann (Mar 26 2020 at 12:24):

Hi all, I recently started working with this start-up in Germany
https://quant-x-sec.com/team.htm
We're doing mostly cryptography : quantum, elliptic curve and isogeny based, that is a lot of algebraic
geometry/topology and CT lurking there. Best, Peter

nadia esquivel márquez (Mar 26 2020 at 15:12):

@Jonathan Beardsley I remember seeing the topic last night but it seems to have disappeared?

Jonathan Beardsley (Mar 26 2020 at 15:14):

I just tagged you in that topic. If you go to "All messages" you should also be able to see it.

Jonathan Beardsley (Mar 26 2020 at 15:14):

Paul Fabel (Mar 26 2020 at 15:51):

I became interested in category theory when exploring the algebraic topology of wild spaces X such as the Hawaiian earring, with particular attention paid to the choice of topology for the corresponding homotopy groups. TOP is often an unsuitable category for such exploration due the general failure in TOP of the product of two sequential spaces to be sequential. Working in a different category such as SEQ turns a bug (failure to be a topological group in TOP) into a feature.

Max Wall (Mar 26 2020 at 16:37):

Hi @Rongmin Lu. Indeed! We had David come speak to us about his work in this area, and I've been puttering around with CQL. Hoping to turn it into more than just puttering with the Conexus folks. As for the prob prog semantics, correct me if I'm wrong, but I think Adam Sciobor does work in this area (see his thesis), and while it may not be semantics outright, I'm also including work on differentiable programming like Conel Elliot's "Compiling with Categories", and Sam Staton's recent work (papers: POPL 2019, FOSSACS 2020).

Bradley Saul (Mar 26 2020 at 16:58):

Hi everyone, I'm a statistician by training. I became interested in category theory by a couple of paths a few months ago, and it's been uphill ever since. I use #functional programming ideas a lot in my work as a statistical programmer using R and Haskell at NoviSci (https://www.novisci.com). Also, I work in the field of causal inference and at some point I found @Brendan Fong 's thesis work, which opened my eyes to the power of monoids.

Noah Chrein (Mar 26 2020 at 17:54):

Hello everyone, I'm a PhD student at the University of Maryland. I'm interested in using category theory to model generic data representation .

I'm also hosting an Applied Category Theory Seminar at UMD, the main theme is hierarchical representation (think topological persistence or operads, etc.) but any ACT topic will be explored. All are welcome! #ACT@UMD seminar

Valeria de Paiva (Mar 26 2020 at 18:54):

hi all, I'm Valeria de Paiva. I'm a category theorist that works on AI and Natural Language Processing, as well as much other cool stuff. well, at least I think it's all cool. I know some friends around here, I think.

Eduardo Ochs (Mar 27 2020 at 03:45):

Bill Bottenberg (Mar 27 2020 at 05:13):

Hi, I’m Bill Bottenberg, physical chemist from long ago. Dr Belluce, my diff e prof persuaded me to go to a seminar at UCR by Saunders McClain in the early ‘70s about Category Theory! Been hooked ever since

Emilio Jesús Gallego Arias (Mar 27 2020 at 06:28):

Hi all! I'm Emilio, a researcher at INRIA / IRIF / Paris 7 (now Université de Paris) I'm trying to make interactive theorem provers easier to use, and I'm interested in categorical logic and mechanization of CT.

Beppe Metere (Mar 27 2020 at 11:23):

Well... there is also that other notion of tangent category https://ncatlab.org/nlab/show/tangent+category which seems to be somehow less investigated. Is out there anyone interested in those? Maybe any ref., other than the ones in the ncatlab page?

Paul Blain Levy (Mar 27 2020 at 12:41):

Paul Blain Levy (Mar 27 2020 at 12:43):

(=_=) (Mar 27 2020 at 12:45):

(=_=) (Mar 27 2020 at 12:46):

Looking at the markdown when I quote and replied your post, I think you've accidentally deleted one of the "`" when you quote and replied my post.

Jelle Herold (Mar 27 2020 at 14:42):

hi I am Jelle, I started the statebox project to try to bring (categorical) diagrammatic methods to programming in the broadest sense of that word. I am a very curious person and have a lot of interests, currently thinking a lot about cryptography and how I can put my skills and our team's experience to best use in what looks like some very bad stuff coming our (the world) way . I wish everyone all the best in these difficult times to come

sarahzrf (Mar 27 2020 at 14:43):

Jelle Herold (Mar 27 2020 at 14:44):

awesome :) we'll be releasing a bunch of code soon and should be revamping the website, to make it a bit more clear what we are actually building, lol

mitchell (Mar 27 2020 at 14:47):

Our organization has been watching Statebox for a while now. Very excited to see what you guys have been up to!

Aleksandar M. Bakic (Mar 27 2020 at 15:00):

Hi, I am Aleksandar Bakic, started reading on applied and computational CT some 20 years ago from the Kestrel Institute papers. Some time later started coding up the pieces I learned in Common Lisp, as I started memorizing less and less. Recently read Seven Sketches, Functorial Data Migration and have been finishing an implementation of Left Kan Extension "directly" by stitching diagrams (using general algorithms, not chase). I work at a startup on unrelated things, have little time for chatting; mostly reading and sometimes coding alone.

Mario Alvarez Picallo (Mar 27 2020 at 22:01):

Hi y'all, I'm Mario Alvarez, recently finished a PhD at Oxford where I used incremental computation as an excuse to do "differential calculus" on discrete spaces. I like programming languages and their (categorical) semantics, Coq, machine learning and the intersection of all of the above. Currently trying to figure out an abstract machine for reverse-mode AD, integration for change actions, and how differential equations and iteration are the same if you squint hard enough.

sarahzrf (Mar 27 2020 at 23:06):

are you Tuplanolla from freenode, or just working on suspiciously similar stuff?

Patrick Elliott (Mar 27 2020 at 23:10):

Hi everyone. I'm Patrick Elliott - I'm a visiting faculty member in the linguistics and philosophy department at MIT; I did my PhD in the linguistics department at University College London. I'm a theoretical semanticist, interested in using ideas from category theory and functional programming to model our knowledge of meaning, with a focus on the logical aspects of the latter. I write haskell, occasionally for work, and also for fun, and I'm interested in learning more about Idris, Agda, and dependently-typed programming languages more generally. SInce this literature is probably unfamiliar to most of you, here's a recent paper I wrote using the Reader monad to model a certain kind of environment sensitivity in natural language! https://ling.auf.net/lingbuzz/005107

Mario Alvarez Picallo (Mar 27 2020 at 23:12):

I'm not them, but it certainly sounds like we should be introduced! Do you know of anything they've written/worked on?

sarahzrf (Mar 27 2020 at 23:18):

[05:49:30] <Putonlalla> Some of you may already know me from #haskell or #coq, but, in short, my gimmick is in trying to harness functional programming for doing computational physics and breaking things as I go.
[06:08:30] <Putonlalla> I am currently working on a type-theoretical model of discrete exterior calculus, which concerns differential forms on simplicial complexes. If this sounds interesting or useful to you, let me know.

sarahzrf (Mar 27 2020 at 23:20):

(i don't actually know anything about the discrete exterior calculus, which is apparently a Known Thing)

John Baez (Mar 27 2020 at 23:21):

Yes, it gets tough when you want a Hodge star operator - many people have thought about that part.

Mario Alvarez Picallo (Mar 27 2020 at 23:28):

Ah very cool! I remember skimming through Grady's book on it once, it's a very different setting from my own, but nonetheless really interesting

Deliciouslytyped (Mar 28 2020 at 18:04):

Hi folks, I'm new o/ :D and I somehow managed to find the topics on the left. :P
I'm interested in functional programing both as a tool and for the fun of it, and I'm currently stumbling through my physics bachelors and looking for excuses to combine physics, mathematics, and computation. (and various related things, as one is wont to do)
So that makes two of us interested in Tuplanolla's work @Mario Alvarez Picallo :)

Badreddine Bouzid (Mar 28 2020 at 19:04):

Hi, I'm Badreddine from Oran University, Algeria. I've used some category theory on the lattice to derive transition rules for 2-connections. I'm been mainly inspired by John Baez, Florian Girelli and Hendryk Pfeiffer works.

Bobby T (Mar 30 2020 at 13:43):

Hi, my name is Bobby Tosswill. I did my undergrad in linguistics at the University of Massachusetts Amherst, and in the last two years I've been trying to dig into category theory, to mixed effect, haha. I found out about this group (and Zulip, if I'm being honest) from a Slack group on category theory in functional programming and figured I might be able to learn a thing or two. I guess I should say ahead of time that just about all of my questions are liable to be stupid ones, haha

Jade Master (Mar 30 2020 at 19:03):

Hi, I'm Jade Master. I'm not sure I'll be able to keep up with all the messages on here but my DM's are open :)

sarahzrf (Mar 30 2020 at 19:13):

Michael Zargham (Mar 30 2020 at 21:12):

Hi, my name is Michael Zargham. I did undergraduate degrees in complex systems (liberal arts) and robotics (b. eng) at Dartmouth, followed by masters in stochastic optimal control at PhD in Networked Dynamic Optimization at Upenn with Ali Jadbabaie (who is now at MIT). I run a private research & design firm which has been working dynamic mechanism design and complementary decision policy design problems. Mathematically we rely on formal methods from CPS, systems engineering and control, most notably i've been working on compositions of invariant preserving mechanisms and configuration spaces for economic systems. I am actively updating my mathematical toolkit with category theory; thanks to @Joshua Tan .

Gabriel Goren Roig (Mar 31 2020 at 04:18):

Hi, I'm Gabo, an undergraduate student from Buenos Aires, Argentina who wants to do a PhD in math, maybe Applied Category Theory if fate permits. I chose to study Physics because I was interested in complex systems, but the usual complex systems work stemming from Physics doesn't have the right level of abstraction for me. My Physics undergraduate degree is extremely long (7 years on average) and has a very inflexible curriculum, so I feel like I've already specialized in something I didn't want to, which... Sucks? It makes me feel that, given my true interests, I "should already know" so many things that I don't... Also no one knows what "Applied Category Theory" is around here, and I haven't had the courage to talk with the few people who do work with categorical things. Anyway, I've been learning some stuff on my own, and even thinking about how to apply CT to a project I've been working on (about finite state automata). I hope to keep learning and perhaps be honored with some useful advice :slight_smile:

Tarun Raheja (Mar 31 2020 at 04:46):

Hi all! I graduated last year (Aug 2019) with a Bachelor's in CS. My research was mostly in canonical CS stuff like complexity theory, algorithm analysis, cryptography and computational geometry during my bachelor's. Then, I spent few months at Microsoft Research.

For my bachelor's thesis I made a switch to computational condensed matter, out of sheer curiosity towards Physics, and have been hooked since. I am now at Prof. Franco Nori's group (Theoretical Quantum Physics Group) in RIKEN, Japan as a funded research assistant for the last six months, and I will spend the rest of this year here as well.

My introduction to Category Theory was through following the work of Prof. Bob Coecke in the Foundations, Structures and Quantum group at Oxford (which I feel is doing some phenomenal work at the intersection of theoretical CS and physics). After this year I plan to apply for a PhD, so hopefully I can find something of interest here!

Tim Hosgood (Mar 31 2020 at 15:28):

hullo, i'm tim, just finishing my phd on simplicial chern-weil theory at marseille/montpellier. is there a stream for algebraic geometry stuff, while i'm here?

(=_=) (Apr 01 2020 at 00:42):

Ariana (Apr 01 2020 at 17:18):

Hi, I'm ariana and will be graduating high school next year:p.
So far I'm focusing on learning commutative algebra and algebraic topology, and occasionally looking into qft with weinberg and doing some cryptography from reading a collection of papers. I'm also focusing quite a bit on music(mainly piano performance) but am looking into neoriemannian harmony and alternative ways of looking at harmony in late/post-romantic music and seems pretty mathematically interesting too.
Still poking into many places and not too sure what to do in the future :laughing:

Preston Sayers (Apr 01 2020 at 18:07):

Hi, my name is Preston and I’m a third year undergraduate interested in various things, but mostly geometry.

John Baez (Apr 01 2020 at 19:09):

Hi @Ariana! Do you know about Alexandre Popoff's discussion group on neoRiemannian harmony theory and other aspects of music theory? It meets on Sundays:

Anyone who wants to discuss math and music theory should join Alexandre Popoff in doing this! He's done great work with Andree Ehresmann and others on category theory in music. Check out his blog: https://alpof.wordpress.com/ and then talk to him here on Twitter.... (1/n) https://twitter.com/johncarlosbaez/status/1241096967779831808/photo/1

- John Carlos Baez (@johncarlosbaez)

Ariana (Apr 01 2020 at 19:13):

Felix Zillinger (Apr 01 2020 at 22:40):

Hi, I‘m Felix and I am an undergraduate at Bonn.
I‘m interested in Algebraic Geometry, -Topology, -Number Theory, Category theory and especially the interplay of all the above. I am currently trying to figure out how to do mathematics and what research field I want to specialize in.

sarahzrf (Apr 01 2020 at 22:51):

Ben Steffan (Apr 01 2020 at 22:54):

Archibald Juniper (Apr 01 2020 at 22:59):

Hi, I'm James, a conjoint at the University of Newcastle of Newcastle, Australia. As an economist with a passion for philosophy (in particular, Schelling, Deleuze, Whitehead, Peirce), I am interested in applications of category theory to macroeconomics, ecological economics, network analysis and, in this era of ubiquitous 'fake news', in finding more democratic modes of communication, cooperative alternatives to private property, and more decentralized and transparent governance structures. One aspect of this is would be the deployment of diagrammatic reasoning (especially, string diagrams) to regain control over machines for as Marx observed, "The hand tool makes the worker independent –posits him as proprietor. Machinery – as fixed capital – posits him as dependent, posits him as appropriated."

sarahzrf (Apr 01 2020 at 23:00):

Ben Steffan (Apr 01 2020 at 23:02):

(=_=) (Apr 02 2020 at 02:16):

Well, clearly, you want to be a student of Peter Scholze then. But so does everyone else. :sweat_smile:

Soichiro Fujii (Apr 02 2020 at 03:39):

Hi, I am Soichiro Fujii, a postdoc at Kyoto University. I am interested in various topics related to category theory, and have worked on a unified framework for various notions of algebraic theory (Lawvere theories, operads, monads, ...) based on monoidal categories, and higher dimensional category (à la Batanin and Leinster).

Joe Moeller (Apr 02 2020 at 06:13):

Soichiro Fujii (Apr 02 2020 at 06:37):

(=_=) (Apr 02 2020 at 06:40):

Felix Zillinger (Apr 02 2020 at 08:37):

@Rongmin Lu I love Bonn, too, not just because of the mathematics that‘s going on, but the city itself is a really nice place to live at.
Yes, obviously I‘d love to be a student of Peter Scholze, but I am aware of the competition. Right now I just enjoy learning about all those fascinating topics, try to do my best and worry about that when the time comes.

Soichiro Fujii (Apr 02 2020 at 09:16):

Helene Finidori (Apr 02 2020 at 11:00):

Hello, I'm Helene Finidori, based in France, engaged in a PhD at Hull University, Center For Systems Studies, in the UK, focused on pattern literacy in support of systems literacy. I am particularly interested in finding interoperability among different forms of patterning/modeling, and looking forward to learn how Category Theory could be put to work in this perspective.

Maxime Lucas (Apr 03 2020 at 08:22):

Hello everyone!
Maxime Lucas here! I am a postdoc at the University of Nantes, France, where I am trying to understand what is going on in HoTT. Apart from that I am working on so-called "higher dimensional rewriting": it turns out that you can use (somewhat) elementary rewriting techniques to compute resolutions of most of your favorite algebraic objects : algebras, operads, etc !
It also allows you to prove some "coherence results" à la MacLane, of the type "every diagram commutes"

(=_=) (Apr 03 2020 at 08:56):

Hi Maxime! Daniel Murfet at Melbourne has used cut elimination to make the computation of matrix factorisations of Landau-Ginzburg models more tractable (paper here). That sounds like something related to what you're doing.

Maxime Lucas (Apr 03 2020 at 09:50):

Rongmin Lu I had never heard of that. Thank you for the reference I'll have a look!

Bobby T (Apr 03 2020 at 10:49):

Oh man, I am fascinated by the whole higher dimensional rewriting thing! If you know any good overviews or state-of-the-art articles, do let me know! Also, welcome aboard!

(=_=) (Apr 03 2020 at 12:03):

You're welcome! Dan's a pretty good algebraic geometer and has worked on some interesting topics.

Maxime Lucas (Apr 03 2020 at 13:20):

Bobby T (Apr 03 2020 at 13:35):

sarahzrf (Apr 04 2020 at 05:50):

Alex Kavvos (Apr 04 2020 at 08:35):

I did! I then wrote a whole thesis on it. I should upload the new version of the paper though, unlike the thesis it's not 230 pages

Cole Comfort (Apr 07 2020 at 04:37):

Hi I am a PhD student at the University of Oxford, and I am currently interested in props. In particular, using the theory of monoidal categories, monads and so on to prove completeness for presentations of various fragments of circuits. I am also interested in reversible computing and the connection to quantum computing.

Sam Tenka (Apr 07 2020 at 05:03):

Hi! I am a PhD student at MIT's computational cognitive science lab. I don't really use categories in my work, but I like learning about math for fun!

(=_=) (Apr 07 2020 at 05:04):

Sam Tenka (Apr 07 2020 at 05:08):

I'm thinking about cognitively inspired program induction! In particular, humans are often able to quickly see what sort of program is needed to solve a problem --- associative thinking from remembered previous solutions helps narrow the search space. How can we get computers to write programs from examples using similar learned heuristics? I sort of just started, though, so this is more a dream than progress.

Before working on that, I was shopping for advisors and doing theoretical machine learning. I developed some "feynman diagrams" for analyzing stochastic gradient descent, and i hope my work gets accepted this year! {Nervous}

(=_=) (Apr 07 2020 at 05:20):

Nice! There's work on one-shot learning that seems like something you could build on.

Sam Tenka (Apr 07 2020 at 05:23):

Thanks! Yeah, that's a good connection. What sort of "sufficient statistic" or "universal essence" should we extract from previously considered tasks in order to inform a new task? There's lots of inspiring work on meta-learning, transfer learning, and hierarchical Bayesian learning that I'm trying to absorb.

As for diagrams, I'd be happy to share a draft (by DM so as not to spam this thread). Thanks for your encouragement!

Reuben Stern (they/them) (Apr 07 2020 at 20:43):

Hi everyone! I'm Reuben (they/them) and I'm finishing my undergrad in math at Harvard this semester. In math, I study homotopy theory, so I'm a user of higher category theory. Recently, my interests have been relating to factorization homology and (secondary) algebraic K-theory. I'm also tangentially interested in categorical logic.

I'll be "leaving math" to pursue a career in orchestral conducting (starting a masters program at the Peabody Conservatory), but I hope to stay in touch with the community :) Once you've spent a long time caring about something, it's impossible to stop caring! So while I may not contribute much, I'm so excited to see the mathematics I care about evolve.

John Baez (Apr 07 2020 at 20:44):

Yeah, it's tough leaving math because people tend to stop paying attention to you... but if you keep talking to people and saying interesting things, you can minimize that problem.

Reuben Stern (they/them) (Apr 07 2020 at 20:48):

Well, I've been perfectly happy without people paying attention to me so far! I'm very happy being a "mathematical cheerleader" -- caring about the people in the field and their successes, and providing emotional support if I can.

Eric M Downes (Apr 08 2020 at 18:24):

Hi everyone. I'm Eric Downes. I work in industry as a data scientist with emphases on cryptography and statistics, usually in python. Really grateful you all are doing this so non-academics like myself can appreciate work we'd otherwise not be exposed to! Thanks John Baez et al!

Piotr Paradziński (lemastero) (Apr 08 2020 at 18:59):

Bar Roytman (Apr 08 2020 at 19:26):

Hello everyone! I'm Bar Roytman. I'm a graduate student at UCLA studying homotopy theory. My interests, broadly speaking, are primarily informed by guiding foundational and computational questions. I'm excited to join this active and diverse community and discuss topics at the core of my motivation as an aspiring mathematician.

Jeremy (Apr 09 2020 at 02:58):

Hi everyone! I'm Jeremy, currently a high school student. I'm particularly interested in algebraic topology and algebraic geometry, and I've recently been reading a lot about homotopy theory and higher category theory, but I like learning anything that I have to struggle to understand. I also like physics, linguistics, and music theory. I’m really excited to meet you all!

Mohamar Rios (Apr 09 2020 at 05:15):

Hi all! I'm Mohamar Rios Flores. I'm a master's student in math at the University of Calgary. I'm interested in non-classical logics, graphical languages, programming language theory, and the way that category theory can be applied to said topics.

John Baez (Apr 09 2020 at 05:39):

Hi, @Jeremy! I'm glad you're here. I hope you enjoy yourself. Right now I'm thinking about the nerve of a monoid, which is a fun thing to think about if you're trying to learn homotopy theory.

Jeremy (Apr 09 2020 at 07:02):

Todd Schmid (he/they) (Apr 12 2020 at 10:18):

Hi! My name is Todd! But the grad students at U of Toronto used to call me Tid, so you can do that too. I am a first-year PhD student in the Programming Principles, Logic, and Verification group at University College London. I am working with Alexandra Silva, David Pym, and Simon Docherty on giving a coalgebraic semantics for reductive logic and proof search (think Inductive Logic Programming). I like the algebraic theory of automata a lot, though I am new to it, and categorical logic. I really appreciate the amount of community I have already found in this forum, and I will try to add to it as much as I can.

Toby Smithe (Apr 12 2020 at 11:44):

Hello friends old and new! I'm a theoretical neuroscience PhD student at Oxford, though I don't like that classification: I'm interested in all kinds of structure, and particularly the structure of our ideas and of systems that might be said to have ideas. So I'm working on a few related projects: a compositional formulation of the "free energy" or "active inference" framework for intelligent systems in the setting of categorical cybernetics; a study of the simplicial structure of certain models of spatial navigation in the hippocampus; and more generally trying to understand the abstract logical structure of the neural code. I call the overarching topic "compositional cognitive cartography": I want to understand how we (and other creatures) explore all kinds of spaces, be they physical or abstract (another distinction that I dislike).

I do like the notion of 'deep' and 'codeep' as adjoint approaches to applied category theory. I'm starting on the 'codeep' side, trying to tunnel deeper. A slightly unfortunate side effect of this is that I've built up a backlog of "papers in drawers" which I really need to write up. I hope to share some of those with you all soon. My feeble excuse is that I prefer working with pencil and paper to working with keyboard and screen.

On the methodological side, I'm attempting to introduce concepts and techniques from theoretical computer science into computational neuroscience (which embarrassingly lacks a notion of 'neural computation'). More generally, these days I repudiate much of the current structure of (scientific) academia into "disciplines" which often seem to bear little relation to the abstract structure of the objects of study. So I also hope to contribute to the effort towards more robust and ecological (more 'autopoietic') structures both in technology and society. Thanks to everyone for building this community!

Fabrizio Genovese (Apr 12 2020 at 12:22):

Toby Smithe (Apr 12 2020 at 12:29):

No, I don't but if you mean this chap, I guess I should send him an e-mail: I have indeed been swotting up on topology lately

Fabrizio Genovese (Apr 12 2020 at 13:05):

That's who I meant! He's one of my best friends. He was using tools from algebraic topology to describe what happens in the brain. I told him more than once that probably category theory would be a nice tool to employ is his research, but I doubt he ever looked into it

(=_=) (Apr 12 2020 at 14:09):

Hi Toby! A couple of people I know have recently been inspired by the simplicial structure of models of spatial navigation to come up with a higher version of the Transformer ANN architecture in machine learning:

I agree that the distinction between physical and abstract spaces is not really a distinction: there is evidence to suggest we transfer our intuition about distances in physical spaces onto abstract spaces.

There is a prejudice, which goes back to a 1989 polemic by a well-known biologist, that computer science cannot inform neuroscience because ANNs are unrealistic. With the benefit of hindsight, this prejudice was founded upon the incomplete knowledge of our brain, and even the name "neuroscience" is a relic of that ignorance. So it is perhaps not surprising that there hasn't been a notion of "neural computation" yet.

Toby Smithe (Apr 12 2020 at 16:42):

Hi @Rongmin Lu: thanks for that link -- I hadn't seen that generalization of the transformer. There are many things to discuss in relation to this topic, but I'll save some of those for another day and another stream. I look forward to talking about them though!

The evidence on this is actually very strong, not just behaviourally but also at the neural level, and I suspect that the abstract notion of "space" -- as a place where stuff happens plus some notions of restriction and gluing -- is actually ontologically prior. But I'm verging on a Platonist.

Labelling this as a prejudice is a step in the right direction, but actually I go a bit further: theoretical computer science, and especially the parts that cross-pollinate with information theory and statistical physics, supplies a lot of very useful conceptual tools to understand "computation" generally (roughly as a kind of dynamics with semantics), and these go well beyond what most lay people (and indeed neuroscientists) think of as "a computer". It is this rather general type of tool and concept that I'm interested in.

Toby Smithe (Apr 12 2020 at 16:43):

@Fabrizio Genovese: very interesting. That toolkit will soon prove very useful in a very broad swathe of neuroscience -- there's even a subfield called "integrative neuroscience" -- and I've recently spent a lot of time studying it. I don't really do any data analysis. My interests are in the theoretical side, both with respect to "how we navigate spaces" (from paths to proofs), and also with respect to notions of natural computation, information-processing in complex systems, and cybernetics broadly.

As many of us have, I've been thinking increasingly about the question of "how to do scientific modelling" and "how to specify models" in such a way that we can translate models across disciplines (as they exist today). At the same time, I think we could do with better tools to assist this: how should this data be represented digitally? How is it represented inside the brain?

Because mathematical spaces are (for me at least) prototypical, I'm trying to figure out how, by stealing ideas from homotopy type theory, we could think about how we navigate (eg) from the premises to the conclusion of a logical deduction. The paper written at the end is a physical artefact witnessing that journey, but along the way the route must have been represented and planned inside the author's brain. And somehow this route should correspond to the abstract witness that exists in some model of type theory.

Rohit Goswami (Apr 12 2020 at 19:33):

Hi all!
I'm Rohit Goswami (https://rgoswami.me)
I'm a graduate researcher at the University of Iceland. I am new to category theory.
My forte is actually High Performance Computing, DFT and ML/AI.

Daniel Geisler (Apr 12 2020 at 23:52):

Hello again, while I use the name Daniel Geisler on here, on Azimuth the name Prashanta, my yogic name, comes up. That's OK because I'm a professional yogi, not a professional mathematician.

(=_=) (Apr 13 2020 at 03:48):

Hi Rohit! DFT (density functional theory) sounds fascinating (I thought it was "discrete Fourier transform" at first). Could you say a little bit more about it?

There's been some tentative steps towards applying CT to ML/AI. The most recent one is this paper by Brendan Fong, David Spivak and Rémy Tuyéras, which abstracts what I believe to be the feedforward network architecture into category theory. That has led to a burst of productivity in ACT: see this blog by Jules Hedges for a round-up of the surprising connections.

(=_=) (Apr 13 2020 at 09:07):

This is the same person who introduced the notion of a "central dogma" in molecular biology. :face_palm:

Let's just say I'm not very impressed with some of the philosophical positions that had been dominant in biology.

Oliver Shetler (Apr 13 2020 at 14:05):

Hi all, I'm Oliver. I'm a grad student at Hunter College, studying statistics and I run an applied category theory meetup.com group called NYC Category Theory. My main reason for studying CT is that it seems like the natural language for my two main long term research interests: computational neuroscience and consciousness studies.

user 170039 (Apr 14 2020 at 07:25):

Hi all, I am a PhD student from India doing my PhD in Mathematical Logic and self-studying category theory due to personal interest. Right now, I am stuck with one particular problem. Where would be an appropriate channel to discuss about it?

user 170039 (Apr 14 2020 at 07:26):

I am also a regular visitor to the sites MathOverflow and Mathematics Stack Exchange. Here are my profile links:

user 170039 (Apr 14 2020 at 07:27):

(=_=) (Apr 14 2020 at 07:32):

James Wood (Apr 14 2020 at 07:45):

user 170039 (Apr 14 2020 at 08:00):

Nick Decroos (Apr 14 2020 at 12:39):

Hello! I'm Nick. I'm an engineer who works as an embedded programmer and electronics designer. I'm mostly an appreciator of ideas. Some things that interest me on the theoretical leaning side: (applied) category theory, PL theory, algebraic statistics, tensor networks, computer vision, control theory.

Pablo Bustillo Vazquez (Apr 15 2020 at 10:30):

Hi all! I'm Pablo. I'm a student from ENS and Cambridge. I just finished my master degree and am taking a year to learn category theory better before doing a phd. I am very interested in foundations of math and of category theory, in higher category theory, (homotopy) type theory, and also just category theory as itself. I'm still trying to find my way in math but I know that those subjects really attract me. I'm working on a few personal projects. To cite a few of my recent interests: I've been recently fascinated by limit doctrines, by codensity monads, by (what I just discovered may be called) directed homotopy type theory, and by necessary conditions for a sheafification existence theorem.

Philipp Zahn (Apr 15 2020 at 12:47):

Hi all! I'm Philipp. I am an economist and interested in applying category theory to economics, mostly game theory and choice theory. In the last years, I have been working with @Jules Hedges on compositional game theory. I am also interested in functional programming.

James Wood (Apr 15 2020 at 13:47):

Have you seen that Dan Licata and Matthew Weaver have a paper accepted to LICS promising a cubical model yielding directed univalence?

sarahzrf (Apr 16 2020 at 04:01):

James Wood (Apr 16 2020 at 07:25):

Univalence is Id(x, y) ≃ (x = y).
Directed univalence is Hom(x, y) ≃ (x → y), where Hom is a thing every type has (like Id), but in the case of a universe, lines up with the (non-dependent) function type. In general, it gives a one-way notion of transportability. In set-level mathematics (or rather, poset-level mathematics), I imagine that it works as a way of enforcing monotonicity over some type.

Reuben Stern (they/them) (Apr 16 2020 at 14:35):

Is there a stream for questions about n-categories (really (\infty, n)-categories)?

(=_=) (Apr 16 2020 at 14:38):

John Baez (Apr 16 2020 at 17:02):

If we get enough discussion of n-categories that we need to separate it off, we can. But that hasn't happened yet.

Pablo Bustillo Vazquez (Apr 17 2020 at 08:20):

dusko (Apr 19 2020 at 02:51):

aloha from the middle of a big ocean. my name is dusko pavlovic and i was invited by fabrizio genovese. i am not sure what might be the important thing to say about myself. this week dominic hughes and i posted this: https://arxiv.org/abs/2004.07353 :)

John Baez (Apr 19 2020 at 03:13):

Hi, Dusko! I haven't heard anything about coronavirus in Hawaii.... hope you're doing okay.

dusko (Apr 19 2020 at 06:15):

Hi John :) Hawaii seems to be doing well with the virus for some reason. People hiking a lot and everyone saying hi to everyone they meet. It feels like an extended holiday at the moment. But I am sure we'll be punished by the economic carnage ahead. Are you home in Riverside? I hope it is less bad than in some other parts of CA.

John Baez (Apr 19 2020 at 06:29):

Yes, I'm in Riverside. This county has considerably fewer detected cases of coronavirus per capita, and a lot fewer deaths per capita, than next-door LA county.

John Baez (Apr 19 2020 at 06:30):

Everyone here is supposed to be wearing face masks outdoors, though not everyone does.

Kevin Arlin (Apr 20 2020 at 17:36):

Hello, I'm Kevin Arlin. I just finished my PhD at UCLA. My research is about higher categories via lower categories-generalizations of Brown representability and suchlike. I used to be named Kevin Carlson.

সায়ন্তন রায় (Apr 22 2020 at 04:37):

Hello, I am Sayantan Roy. I am a first year PhD student at IIITD, India. My area of interest are mainly Mathematical Logic and Foundations of Mathematics. I am self studying Category Theory due to personal interest.

John Baez (Apr 22 2020 at 05:09):

Thomas Greco (Apr 24 2020 at 13:52):

hey! thomas greco here... based in NYC where I work as a software engineer. more specifically, i spend my days building trading apps for a fin institution in the city. I was introduced to category theory thru the functional programming paradigm and since then have been constantly seeking out new knowledge on the topic! excited to be in this group :)

Sophia Restad (Apr 24 2020 at 14:24):

Hello everyone! I'm Sophia, a PhD student at Kansas State University. My research is in derived algebraic geometry and (increasingly) higher category theory.

Sam Kuhn (Apr 24 2020 at 14:26):

Hi All, I'm pretty new to Category Theory and have a (possibly unrealistic) hope that by hanging out for a while some wisdom might rub off ;) I'm also intrigued by the idea of applying aspects of CT to a 3D content authoring platform that I'm currently working on.

Morgan Rogers (he/him) (Apr 24 2020 at 14:35):

@Sam Kuhn have a look at this topic and let us know what your project is all about :grinning:

eric brunner (Apr 24 2020 at 14:46):

Sam Kuhn (Apr 24 2020 at 14:55):

Thanks @Morgan Rogers I will take a proper look in a bit. Having quickly skimmed it seems to be a discussion around the concept of embedding mathematical (and other) artefacts directly into scientific papers so they be referenced directly? (If I'm understanding correctly)

Sam Kuhn (Apr 24 2020 at 14:57):

And sure I'll post some info on my project when I get a bit of free time. Thanks!

Henri Tuhola (Apr 24 2020 at 15:13):

Hi, I'm a hobbyist exploring programming language theory. I usually lurk around in r/programminglanguages at reddit, but recently CT has taken bit of stage in what I am doing.

Henri Tuhola (Apr 24 2020 at 15:15):

Writing a blog https://boxbase.org/ about the last 3 or 4 posts are about category theory.

Henri Tuhola (Apr 24 2020 at 15:16):

I first found CT really hard topic to approach, now I've found it really hard topic to write about.

(=_=) (Apr 24 2020 at 15:18):

(=_=) (Apr 24 2020 at 15:26):

I started that topic, so it's interesting to see how much it's evolved since then...

Re. embedding mathematical artifacts in papers, that has been accomplished by

\TeX

and

\LaTeX

. My initial intent was to discuss an article about redesigning papers to make it visually more enticing and informative.

The conversation subsequently morphed into how to process automatically the vast amount of information currently stored in scientific publications into some sort of semantic network (both within the paper itself and with other papers), and how this can facilitate better quality control and assurance in scientific publishing.

(=_=) (Apr 24 2020 at 15:31):

I'm aware of a similar project that billed itself as a Github for engineers (of the non-software kind), so your platform sounds really interesting!

Sam Kuhn (Apr 24 2020 at 15:40):

Thanks for the clarification @Rongmin Lu - very interesting and I hope to read it through this evening. Also for linking to Stemn I wasn't aware of it at all and it seems very much the same ballpark.

(=_=) (Apr 24 2020 at 15:47):

It's a new project based on another continent, so I'd be amazed if you're aware of it.

John van de Wetering (Apr 24 2020 at 16:56):

Hi all, I'm a PhD student working in quantum theory, with some interest in how category theory can be used for quantum physics and mathematical physics related subjects

Jacques Carette (Apr 24 2020 at 17:02):

I'm a CS prof who was formally educated as a mathematician (specializing in analysis and complex dynamics), worked professionally in symbolic computation (Maple) for 11 years, before returning to academia. I'm extremely interested in 'mechanized mathematics'. As should be no surprise to anyone here, meta-mathematics is full of categorical "stuff", which I'm trying hard to leverage to good use. I have gotten bitten hard (in a good way) by a few things in the last few years: category theory, dependent types and meta-programming. One day, I will manage to stuff all 3 in the same paper.

John Baez (Apr 24 2020 at 23:34):

Mukesh Tiwari (Apr 25 2020 at 07:30):

Hi everyone, I am Postdoc at the University of Melbourne and interested in formal verification (Coq theorem prover) of electronic voting and cryptographic protocols. I am interested in Category theory because I want to use it as as a tool to understand (make elegant) other concepts.

Daedalus (Apr 25 2020 at 20:46):

Hi. My name's Dean and I'm finishing a degree in mathematical physics at Heriot-Watt University in Edinburgh. I recently just submitted a dissertation in semigroup theory, where most of the research I did into the literature of the subject involved abstract notions from category theory. At my confusion, I decided to begin learning some. So here I am. :^)

Jalex Stark (Apr 25 2020 at 23:49):

I work as a researcher at a trading firm. I used to be a grad student proving theorems about quantum computing. Now my academic interests cluster around the question "how do we leverage technology to accelerate mathematics research, including via new communication methods and via changing incentive structures?" I hang out a lot on the leanprover chat.

I'm currently thinking about approaches to tame the constructions of MIP* = RE using categories. (To give a sense of what stage it's at, I have a category of "games" and "simulations" such that the product and coproduct in this category correspond to some of the constructions in the CS literature. I haven't yet proven that the natural map from games to C^*-algebras is functorial. I think that the "introspection game" from the MIP^* = RE paper will end up being an exponential object in this category.)

Arthur Parzygnat (Apr 26 2020 at 11:59):

Hello, everybody! I'm currently a postdoc and work on information theory, probability theory, quantum mechanics, and occasionally other areas like differential geometry, algebraic topology, and condensed matter, though less in recent years. Lately, I've been thinking about Bayes' theorem in a quantum context, and I spend a lot of time doing linear algebra. It's amazing to see so many people here!

Sam Tenka (Apr 26 2020 at 18:36):

Hi @Arthur Parzygnat! Nice to meet you! Have you seen @Brendan Fong, @Tobias Fritz, or @John Baez's work on probability theory and Bayes rule? I'm not sure there is yet a probability channel (the closest matches seem to be

Arthur Parzygnat (Apr 26 2020 at 18:48):

Hi @Sam Tenka (naive student) ! Thanks again for the invite and nice to meet you, too. I'm aware of their work (at least I think I am---I guess it's possible I've missed some things!). I discovered the "causal inference" topic, but didn't notice the other two you mentioned, so thanks!

Daniel Geisler (Apr 26 2020 at 20:14):

Best wishes, but I don't belong here. I'm moderately autistic and folks can't understand me.

sarahzrf (Apr 26 2020 at 20:15):

Henry Story (Apr 26 2020 at 20:26):

I am not sure if I used to be autistic or not, but what I know of it comes from Philosophy of Mind, where some have associated it with a problem of intersubjectivity. If that is right and for those that are mathematically inclined, then I think modal logics could help. I wrote a blog post 12 years ago are OO languages Autistic?.

Oliver Shetler (Apr 26 2020 at 20:29):

Arthur Parzygnat (Apr 26 2020 at 20:35):

I suspect anyone can do this. I will try, and if you don't see a "topic" called "Probability and statistics" within the next few minutes, this means I have failed. Update: The topic will be under the stream "practice: applied ct" Update 2: wow that was easier than I expected :sweat_smile:

Todd Trimble (Apr 26 2020 at 23:10):

Daniel, my son (also named Daniel) is on the spectrum. I hope you don't give up on the community just yet. And I hope the community finds more ways of demonstrating support.

Oliver Shetler (Apr 27 2020 at 01:16):

@Daniel Geisler, I am quite far from being on the spectrum but I can also feel weird on forums. There is something about the faux emoji based intimacy mixed with collegial formality that makes forums a recipe for feeling misunderstood. You are not alone in feeling that way! However, the phenomenon structural, not personal! It's something everybody is adapting to. I hope you stick around though! There are so many cool things going on here.

Benoit Valiron (Apr 28 2020 at 11:58):

Hi, my name is Benoit Valiron. I am researcher in computer science at Université Paris Saclay, working in semantics of linear logic, quantum computation and algebraic structures in general. I got tricked by @Aleks Kissinger into joining :wink:

Jon Sterling (Apr 29 2020 at 17:01):

Hello everyone, I am Jon Sterling, a phd student in computer science working on Homotopy Type Theory and related topics. I am applying category theory to logic and computer science, but I currently almost exclusively work on the "universal property" style of applied category theory and not the "monoidal structure" side. I am currently interested in learning more about infinity categories and infinity topoi.

My research is currently focused on what I refer to as the Objective Metatheory of dependent type theory, using invariant, conceptual, and categorical methods to replace intractable problems of syntax by tractable problems of semantics. I am also an implementer of proof assistants.

sarahzrf (Apr 29 2020 at 17:02):

Jon Sterling (Apr 29 2020 at 17:03):

Cody Roux (Apr 30 2020 at 01:56):

Jon Sterling (Apr 30 2020 at 14:00):

sarahzrf (Apr 30 2020 at 14:31):

me too actually, ive been meaning for ages to learn something about nuprl-style type theories

sarahzrf (Apr 30 2020 at 14:31):

Jon Sterling (Apr 30 2020 at 14:33):

Perhaps then it would be a good time for me to dissuade you from learning too much about those haha ;-)

Jon Sterling (Apr 30 2020 at 14:35):

Not to be overly negative, but my interests now are different from what they were when I was working on those, and I think that unfortunately Nuprl-style type theory can have zero application to my current areas of interest, both for some simple reasons that are well-understood and for some complex reasons that are poorly understood. I don't have time to go into it right now though.

sarahzrf (Apr 30 2020 at 14:36):

thats actually good because i have other stuff i really need to be working on rn

Jon Sterling (Apr 30 2020 at 14:37):

I have great respect for the Nuprl project as one of the first serious type theoretic proof assistants, and also because they came up with a lot of ideas that are now "standard" and whose origins are sadly forgotten. The specifics of Nuprl, though, are maybe best left to the shadows of history and a better way to pay it respect is to follow in the legacy by creating new and fun tools based on type theory.

Sam Tenka (Apr 30 2020 at 17:21):

the "universal property" style of applied category theory and not the "monoidal structure" side

@Jonathan Sterling ooh! I haven't encountered this distinction before! Are there good examples of this cultural spectrum?

John Baez (Apr 30 2020 at 17:56):

The famous Abramsky-Coecke paper on quantum protocols instigated a huge line of work (based in Oxford) on pictorial approaches to quantum mechanics - this is in the "monoidal structure" side.

John Baez (Apr 30 2020 at 17:57):

Jon Sterling (Apr 30 2020 at 18:01):

And to be clear, I don't want to be sectarian about this and start painting people into corners ;-) All I will say is that for the kinds of questions I am currently interested in, the main leverage of category theory for me has been in the emphasis of universal properties and distinguishing the parts of disciplines-of-application that require some creativity from the aspects that are "trivially trivial" (a matter of paperwork).

Category theory is also amazingly well-adapted as a language for organizing complex structures that are not universal, and this aspect of the application of category theory (often under the banner of compositionality) is a fast-growing and fascinating area of research about which I am not currently an expert.

John Baez (Apr 30 2020 at 18:06):

My own work on network theory is also largely in the "monoidal structure" side; try Network Theory for a range of examples. Brendan Fong's thesis, available there, is a good introduction to the key ideas.

vikraman (Apr 30 2020 at 18:41):

I'd also like to point out that there is an intersection between the "universal property" style of CT and monoidal structures, one can use tools from formal CT to study monoidal structures in Cat. a nice example is this note about 2-categorical day convolution, and also the constructions related to generalised species. Some of us who are Marcelo's students are working on related problems :-)

John Baez (Apr 30 2020 at 19:03):

Yes, there's a lot of overlap and there will be more in the future. For example, my more recent work on networks starts using "universal property" ideas more heavily:

Already using left adjoints instead of lax monoidal functors makes structured cospans easier to set up than decorated cospans. But the serious business starts when we show structured cospans are morphisms in a weak category internal to Rex, the 2-category of finitely cocomplete categories and right exact functors.

Jon Sterling (Apr 30 2020 at 20:53):

@John Baez Sounds very cool! At some point I'd like to do a bit of a deep dive and see what this stuff is all about. My experience is that to really get my hooks into a topic, I need it to affect one of my "pet problems", so I'll have to be a bit creative :)

John Baez (Apr 30 2020 at 21:08):

There are by now quite a few talks online about this stuff, so it's pretty easy to get started.

sarahzrf (May 09 2020 at 01:00):

is there a way to get this topic pinned so that ppl will se it first thing when they join?

Nathanael Arkor (May 09 2020 at 01:06):

Simon Burton (May 12 2020 at 19:10):

Hi everyone. I am a theoretical physicist working on quantum codes, which is a subfield of quantum computing. It's generally accepted that quantum computers will eventually need to use some kind of codes to protect the precious qubits. By another example of the weird efficacy of mathematics in physics, the most promising quantum code comes from (is?) the cellular homology of a 2-dimensional manifold. And this idea overlaps with condensed matter physics: such a "code" can be seen as a simple example of a 2d topological quantum field theory. So while I wait for someone to actually build one of these things, I get to think about a lot of cool mathematics, much of which involves category theory.

I also have a semi-regular collaboration going on with James Dolan. James is interested in categorified algebraic geometry, homotopy theory and the Langlands program. These big ideas are so big, possibly eating all of mathematics, I have a suspicion that they also have a lot to do with quantum computing. We will see.

Tomáš Gonda (May 16 2020 at 04:12):

Hi all, it's nice to see a vibrant community here, random science discussions are among the things I miss the most these days! :upside_down:

I am a phd student at the Perimeter Institute. Broadly speaking, I am interested in abstracting techniques and methods used in (quantum) information theory, both for the purposes of better understanding the physics, but also more generally to map out the science methodology at play. A bit more specifically, I think about resource theories, as they offer a nice way to understand physics from a more agent-centric and less reductionist perspective, in contrast to the classic narratives. As such, I would like to extract the lessons learned in this context and see where they lead.

Other than that, I am also interested in causal inference, both in the classical and quantum domain.

Nikolaj Kuntner (May 17 2020 at 16:25):

Hello, I'm Nikolaj Kuntner. I usually say I got a PhD in physics (officially it's in aerospace engineering, practically it's in plasma chemistry, but I did my masters in something like Riemannian geometry derived from Matrix models). I currently work in computer vision for a US company, so I might be responsible for the SO(3)-representation elements being multiplied on your phone once you turn on some apps. Funfact, to compute the opening angle of a rotation it might pass from a 4-component quaternion to a 3x3-rotation matrix, simply because the relevant functions are already there and the risk of messing something up by attempting to map from the quaternion to the angle directly are not worth it. I have a vlog (https://youtu.be/E7V36JvHbsA), implementing this and that, trying to be a little more general and explicit about the underlying theory that's used. I interacted with a lot of people here before, on the nForum, or the distributed computing space, etc., but I also see a lot of names now that I don't know, so here's my Introduce Yourself.

Joscha Diehl (May 18 2020 at 16:13):

Hi everyone, I am Joscha Diehl from Greifswald (https://diehlj.github.io/). Coming from Stochastic Analysis I'm interested in (noncommutative) algebras since they serve as book-keeping devices for various things there (the prime example being iterated integrals). This year I am looking into operads and homological algebra, to get a broader view on things. Happy to discuss noncommutative, nonassociative algebras, operads, as well as TDA!

David Michael Roberts (May 26 2020 at 23:14):

@Nikolaj Kuntner heh, I like your technique of putting random images as the still on your YouTube videos. Makes them eye-catching.

Nikolaj Kuntner (May 26 2020 at 23:25):

John Urbanik (he) (S1'20) (May 27 2020 at 19:37):

Hey all. I'm a data scientist with a electrical engineering background (information theory, graph theory, bayesian statistics) with a pretty weak background in category theory and abstract math in general; I've always been an applications first person. I've found that my intuitions often line up with abstractions from category theory, but that I don't always have the mathematical language to realize that! I'm working through Riehl, Fong, and Spivak's books in order to rectify that terminology gap and so I can understand the elegance of some results from category theory more formally.

Domains that I'm interested in that I think category theory can bring some nice abstractions to: include causal inference/ probabilistic graphical models and network theory (especially directed hypergraphs, networks of oscillators, complex adaptive systems). I'm particularly interested in the applications to meta-science (think https://www.darpa.mil/program/automating-scientific-knowledge-extraction) and to dynamical systems work in computational epidemiology, biology, and neuroscience. As such, super interested in sheaf theory, topos theory, hodge theory, and (stochastic) petri nets. I've been eagerly playing with the tools built by James Fairbanks (and the rest of the Julia community) and reading all the work from Fong, Spivak, Tuyveras, Baez, and now Evan Patterson's thesis in a hand-wavey fashion, and hoping to go back later with some more rigor.

Kyle Raftogianis (May 28 2020 at 18:55):

Hi everyone! I'm a software engineer by trade, but I have some background in type theory and category theory. Right now I'm working on formal verification of computer systems, and exploring everything related to that (proof assistants, semantics of programming languages, distributed computer systems, even physics!). I'm excited to meet you all! :slight_smile:

Peter Arndt (May 29 2020 at 02:40):

Hi, I did a PhD in motivic homotopy theory, but have been skipping around Homotopy type theory, non-classical propositional logics, the outskirts of number theory, like quadratic forms and the field with one element. And I love topos theoy! I just became a lecturer in computer science at Düsseldorf, Germany. I am not much of a computer scientist yet, but I am trying to become a valuable member of my department (or at least not the lamest duck) - so I want to learn about Topological Data Analysis, and all kinds of applications of category theory in computer science. Especially if they are AI or data science related. I don't think many people in my department know what a category is, so I am grateful for story lines that start in very concrete computer science situations and lead naturally and/or successfully to category theory...

Simon Burton (Jun 01 2020 at 13:22):

Have you thought about a resource theory being a functor ? It would have codomain the positive reals (with

\le

as morphisms) and domain a category of quantum density matrices and CP maps (or something like that)... I'm wondering if anyone has thought about resource theories with codomain some other POSET's.

Simon Burton (Jun 01 2020 at 13:28):

Also, these functors don't seem to be monoidal, but they do obey a "sub-monoidal" equation:

F(\rho\otimes\sigma) \le F(\rho)\otimes F(\sigma).

I wonder if the cateogory theorists have a name for such a thing. Here I'm thinking of the codomain of

F

(\mathbb{R}^+,\le,+,0)

as a monoidal category.

Nathanael Arkor (Jun 01 2020 at 14:01):

Simon Burton (Jun 01 2020 at 14:03):

Aha! Thanks.. And now I know what a lax monoidal functor is, or at least one example thereof.

Ben Sprott (Jun 02 2020 at 02:01):

Hi Everyone,
I am an automation developer that has just launched a new startup applying Category Theory to AI for Industrial environments. I have an MSc in Physics from Waterloo and was a member of PI as a student. I also have an MSc n Computer Science. I also work on foundations of physics and science using Category Theory. You can see my papers here: https://www.researchgate.net/profile/Ben_Sprott.

Jules Hedges (Jun 02 2020 at 09:52):

This sounds cool! Can you describe roughly how the use of category theory translates into business advantage?

Ben Sprott (Jun 03 2020 at 20:46):

Hi Jules,
Our hope, at Cavenwell AI, is that Category Theory, and especially it's role in the foundation of data science, can help companies automatically learn the overall theory for their products, be they physical or software systems. I liken the application of Cavenwell AI to industrial settings to that point in the history of science between the basic work on understanding electricity and the development of Maxwell's Equations. Companies do not have concise theories for their products. Rather, they have the application of the myriad of scientific disciplines to localized facets of their products. We hope to empower their scientists and engineers to more completely understand, and thus improve, their products.

Jules Hedges (Jun 03 2020 at 20:50):

Fabrizio Genovese (Jun 03 2020 at 21:46):

Ben Sprott (Jun 04 2020 at 01:28):

We are developing a software system and an interactive assistant that would be used directly by a customer.

Rob Spekkens (Jun 06 2020 at 04:22):

Hi, I'm a faculty member at the Perimeter Institute for Theoretical Physics working mostly on the foundations of quantum theory. I work on causal inference, contextuality, nonlocality, information theory, thermodynamics, symmetry, and resource theories. I'll be speaking about how to unscramble the omelette of inferential and causal concepts in classical and quantum theories.

Dhruva Divate (Jun 11 2020 at 12:51):

Hey there,
I am Dhruva Divate a student in the MSc Mathematical Physics programme at the Uni of Tübingen. I am working on my Master's thesis on Topological Hochschild Homology.

Bob Haugen (Jun 14 2020 at 17:51):

I'm an outlier. I'm a very old man. And I am not academic, and don't know very much Category Theory, but I have a hunch it is related to our work, which is why I am here observing this delightful forum.

I am part of http://mikorizal.org/ - we work with live groups who are experimenting with new economic relationships, sorta sloppy participatory action research. Here's what we are working on now: http://mikorizal.org/futures.html

If anybody who knows category theory sees anything interesting in there for a really applied CT project, I'd be delighted to work with you on it.

Timothy Xu (Jun 16 2020 at 19:14):

I have just finished my bachelor's at UC Santa Barbara and will start an MSc in pure maths at either NYU or Imperial (pending Imperial's decision). I have just done a course in category theory with Prof. Stephen Bigelow using Fong & Spivak and Riehl and that is so far all I know about categories, but I am intrigued and am looking forward to learn more!

John Baez (Jun 16 2020 at 19:18):

(=_=) (Jun 17 2020 at 04:13):

Hi Timothy! Welcome! I took a short course with Stephen when he was one of the lecturers, together with Mark Kisin, in the Algebraic Structures stream of the inaugural AMSI Winter School at the University of Queensland back in 2004. I think he taught some representation theory and Mark taught some number theory. Good times!

Avi Craimer (Jun 19 2020 at 17:55):

I have a background in academic philosophy and currently work in industry as a front-end developer. I have been self-studying category theory for about year. I just finished the 4-day CT training offered by Statebox.

I'm quite interested in helping to develop graphical UIs for diagrammatic reasoning. I'm also interested in using category theory to build tools to aid with thinking in non-mathematical fields.

Andrew Shulaev (Jun 20 2020 at 22:59):

Hi, I'm a software engineer interested in functional programming and type theory. I know a little bit of category theory and joined this server to participate in discussions in the new categorical statistics reading group: I've got interested in statistics quite recently after finding out that causal inference is a thing and getting really interested in it. Since the idea of making connections to other areas is really appealing to me, I would like to learn how category theory applies to this area.

ADITTYA CHAUDHURI (Jul 04 2020 at 09:33):

Hi everyone, I am a 2nd year PhD student in Mathematics at IISER, Thiruvananthapuram, India. I am learning Higher Gauge Theory and Higher Geometry mainly from the work of Baez, Schreiber , Waldorf, Wockel, Bartels, Jurco, Nikolaus among others. Recently I started working on a problem in this area. Till now I am only using the ideas of upto 2-categories. But in future I want to use the ideas of Higher categories i.e n-categories and infinity categories in my work . I have seen some papers which uses the higher categorical ideas but currently I am not equipped well with the machineries needed to understand those concepts. I am trying to learn infinity categories from Kerodon (Lurie) but I am feeling it is very dense and it will take a long time for me to understand these higher categorical ideas. I am also reading parts of Introduction to Language of Stacks and Gerbes by Moerdijk suggested from An Invitation to Higher Gauge Theory by Baez and Huerta to understand about Non trivial 2 -bundles. Also I am interested in Homotopy theory and Model categories. Lastly I am very much interested in using the abstract ideas of Pure Mathematics to tackle Real World Problems. So Learning some Category Theory and Learning how to apply ideas of the same in Real World are my greatest motivation to join this community.

Alejandro Díaz-Caro (Jul 04 2020 at 13:05):

Hi there. I am professor at Quilmes University and researcher at ICC (Buenos Aires University), both in Argentina. I work mostly in lambda calculus, type theory and quantum computing, and I have started to work in categorical models, thanks to Octavio Malherbe, from Uruguay, who introduced me to the area. Now we have two phd students in co-direction: Rafael Romero and Malena Ivnisky, following up with our collaboration!

John Baez (Jul 04 2020 at 16:36):

Hi! Good. I'm not working on higher gauge theory right now, but a lot of work on it uses

(\infty,1)

-categories.

Deepak Vaid (Jul 05 2020 at 16:42):

Hello everyone. I'm an Asst Prof in Physics working at the National Institute of Technology Karnataka (NITK) India. I work in quantum gravity and high energy theory. I favor the Loop Quantum Gravity approach over String Theory, though I'm working on understanding their similarities and connections. My interest in Category theory started as a curiosity as an undergrad some 17 years ago, but only matured into a serious interest over the past couple of years when I realized that it can possibly provide a unifying language for quantum gravity. I also write a blog at https://www.quantumofgravity.com/blog on various topics in high energy physics.

Ben Hicks (Jul 05 2020 at 22:55):

Hello everyone, I am a fresh (1 week) PhD student with UTS in Australia. I have a background in education / mathematics and I've been delving into Learning Analytics and various educational data sets. I'm hoping to apply CT to the problem of context in an analysis / study - so basically if the framework of CT can help articulate the issues of moving between spaces like the 'real world' and 'data' and if what is lost / gained along the way has implications for trust in the end result. I feel like just the language of CT might help, but I'm also hoping that it might be applicable enough to solve some problems directly. (Just caught 1/2 of the tutorial day for ACT2020 and it was excellent)

Filip Buric (Jul 06 2020 at 15:52):

Hi! I’m a PhD student in data-driven systems biology at the Chalmers University of Technology, Sweden. My background is in theoretical computer science (BSc) and complex adaptive systems (MSc). While I’m enthusiastic about many things, my current focus is on modelling living systems. My thesis project involves characterising the proteome (the set of proteins and their interactions) in yeast cells. A parallel (and more long-term) interest is in bridging / reconciling different types of models and frameworks.

Hudson Pepper (Jul 06 2020 at 15:57):

Hello! I am a Physics and Math double major at Penn State University in the US. I am currently doing work for a company in natural language processing and conceptual representation. I am fairly new to category theory, so all of my knowledge is self-taught from papers and books online. I am attempting to apply it to bridge the gap between these two different representations in AI.

David Lyons (Jul 06 2020 at 18:10):

Hi everyone. I am not a mathematician at all, I'm a data engineer but my interests in databases and functional programming brought applied category theory to my attention and so I've been checking out the tutorials from Sunday as well as @John Baez Azimuth course from 2018 and Seven Sketches. Open to any recommendations for other material that offers a gentle learning curve, especially if it talks about ACT as a framework for thinking about databases and functional programming in an elegant way.

Nivedita (Jul 06 2020 at 19:39):

I'm a final year undergraduate at IIT Kanpur (India) My majors is Material Science, but in the last four years I've dabbled a lot, from theoretical condensed matter physics (clean and random Ising), Knot Theory(Khovanov Homology, Ribbon Categories), Gauge Theory (fibre bundles formulation, leading up to getting polynomial invariants from Chern Simmons); TQFTs (Entanglement Entropy calculations using the Atiyah definition of TQFT), classification of defects (using Homotopy Theory, inspired form Mermin's result), one constant in all projects or readings I undertook and even currently am is Category Theory. Since, I'm an Engineer by degree (just graduated) doing so much CT made me feel different from the rest of my class. I am also very driven towards Cognitive Science and Neuroscience and I keep looking for bridges and ways CT can be made a language neuroscientists can think in, (in my dreams I feel this will bring Grothendieck like revolution to the field) So far I've found some works which try to aim in the direction by Gomez Ramirez, Brown and Porter, Andrée Ehresmann. But, I feel very anxious because I don't know where do I fit in and if I will be able to contribute as much I feel driven to, further in academia.
I can't even ascertain the departments I should apply to for Grad school, especially given the COVID scenario, the uncertainty has increased many-fold (manifold? anyone) When I came across this conference, thanks to the smart AI of Google who learned from my searches and recommended ACT2020 in my feed, I was delighted. This is the best thing to experience sitting at home. Thanks to the organizers.
I would love to have any pointers from anyone present here as to how I (as an engineer, who used to make flexible printed electronics) should go forward touching neuroscience and physics simultaneously with CT sword in my hard (which needs a lot of brushing, sharpening because in this group I probably know the least CT).

Chetan Vuppulury (Jul 07 2020 at 09:41):

Hi! I have just finished my undergrad in Physics and Masters in mathematics at IIT Kanpur, India. I have been reading diverse things in the CT landscape including synthetic differential geometry, HoTT, higher gauge theory, TQFT (my Master's thesis was on the Cobordism Hypothesis and implications of it) as well more traditional topics in math and physics such as AdS/CFT and other stuff in Algebraic Topology and Algebraic Geometry. I've been learning the machinery of

(\infty,1)

-categories from various sources. Schreiber's Differential Cohomology in a Cohesive

\infty

-topos has been on my bucket list for a very long time now.

Other than this I'm also very interested in theoretical computer science, randomness and entropy, linguistics and philosophy. I'm looking for groups where my interests would fit in to join as a PhD student.

Alex Hoffnung (Jul 07 2020 at 14:35):

Hello. I’m Alex Hoffnung, a category theorist working in fintech, living in New Haven, Ct. I’m always happy to talk CT with people (and Ct people). I’m interested in math pedagogy and human/social processes. I tend to enjoy thinking across disciplines and category theory has provided nice frameworks for that. Glad to be here!

ADITTYA CHAUDHURI (Jul 07 2020 at 17:50):

Hi Alex! I am Adittya, currently a 2nd Year Phd student from India working in the area of Higher Gauge Theory . I especially liked "I’m interested in math pedagogy and human/social processes. I tend to enjoy thinking across disciplines and category theory has provided nice frameworks for that." Personally I am also curious about understanding human/social Process but I do not have much idea about how to approach it using category theory. It would be a real pleasure if you kindly share about your views/thoughts in this regard! Thank you!

John Baez (Jul 07 2020 at 19:19):

Hi! Maybe you should start a reading group with @ADITTYA CHAUDHURI, who is interested in this too. He's talking about higher gauge theory here.

ADITTYA CHAUDHURI (Jul 07 2020 at 19:48):

Utih Amartiwi (Jul 10 2020 at 13:13):

Hello! I'm Utih from Indonesia, I did my bachelor in pure mathematics and currently I'm master student in data science, Innopolis university, Russia. I'm still learning how to apply category theory in data science/statistics/NLP. This is my bachelor research about abelian category theory abelian-property-of-the-category-of-u-complexes.pdf

Erik Post (Jul 10 2020 at 17:13):

Hey folks! I'm Erik and I'm a software developer at Statebox based near Amsterdam. I got interested in CT through functional programming, and have been hooked since I first learned what a functor was.

To throw out some things I'm interested in: programming languages and methods, computation, databases, music, literature, forest walks, many things medieval, petting sufficiently small animals, and lately also topology and assorted topics in economics, physics, etc.

I've met a good number of you around Oxford, Schoorl, Tallinn, Berlin, etc. and it's been a pleasure. It's very nice to see familiar names and faces around here, as well as unfamiliar ones, and I look forward to lurking around and talking morphisms and whatnot.

Ellis D. Cooper (Jul 10 2020 at 18:00):

In a set theory course at Columbia University in around 1967, my friend Nick Yus introduced me to category theory via algebraic topology. A couple of years later, Ralph Abraham introduced me to Lawvere (in a Parisian pub). In 1968 I audited a course on category theory given by Samuel Eilenberg. In Summer 1969 I attended the Summer Seminar in Category Theory at Bowdoin College, where I attended the lectures by Saunders Mac Lane (where he presented my example of continuous map as an adjunction). By Fall 1969 I was enrolled as a student of Lawvere at Dalhousie University. My best friend was Radu Diaconescu. I did not impress Lawvere much at all, and I went over to be mentored by Barry Mitchell. We became friends over ensuing decades, mostly by telephone. A couple of years ago he said, "You know, back then you were not as good as you thought you were." This sort of hurt my feelings, except that I do not recall thinking myself as good at mathematics. Enthusiastic, way yes, quick-minded, not. I am still enthusiastic. My passion is to categorize my choice of modern theoretical biology, the part of systems biology that leaves genetic reductionism aside, and moves to the realm of biological autonomy. The first step is to take care of adequately explaining micro and macro thermodynamics. Then there is the matter of explicating a recent foundational principle called "closure of constraints."

Nick Bathum (Jul 11 2020 at 18:30):

Hello, I'm from the industry side, in software. Currently working at rjginc.com where we enable process analysis and machine control for plastic injection molding. Besides some java programming, mostly what I'm doing day to day is designing software systems and helping coordinate between teams. Long time fan of functional programming, written some (very basic) Haskell. So I'm glad to have found Bartosz Milewski's blog and videos to work through. I'm inclined to learn category theory so I can finally understand haskell :P, and also inspired by things like the Azimuth project, and plus its just fun.
edit to add
Big fan of NixOS, a GNU/Linux distro composed of software packages defined in the nix language (https://nixos.org/). Highly recommend it, if you have trouble managing software dependencies. This way you can have those same problems but at a higher level :) also if you are more free software or LISP minded, there is https://guix.gnu.org/

Matt Peddie (Jul 14 2020 at 00:14):

Hello all, I'm an aerospace engineer / programmer working at kittyhawk.aero on manned electric aircraft (mostly in Haskell). I don't know a lot of category theory (or math outside of linear systems theory), but some of my coworkers (@Chris McKinlay @Greg Pfeil ) have demonstrated to me how useful a theoretical approach can be for many practical software problems, so I'm here to learn more.

Posina Venkata Rayudu (Jul 16 2020 at 06:20):

Hi, this is posina. I'm calculating the space of all mathematical answers to the question: What is consciousness?

dan pittman (Jul 25 2020 at 17:51):

Joseph Denman (Jul 31 2020 at 22:30):

This is my first time saying anything here, so "Introduce Yourself" seems appropriate. I'm Joe. This server is an incredible resource.

Also, I have a question, but I'm unsure where to put it, so I'll leave it to a moderator to categorize. My question is, why does the diagram for equalizers differ from the diagram you get when you create it by taking the limit of a formal diagram, i.e., a functor? This is the typical diagram for equalizers:

As a side note, I find it interesting that the syntactical representation of the categorical product distinguishes both targets of the cone legs. That is, in the product A x B, both constituent objects appear. This allows us to define the functors like - x B, which is left adjoint to the exponential (_)^B. Equalizers, on the other hand, are not syntactically represented as the composite of two objects.

Joseph Denman (Jul 31 2020 at 23:31):

If we make the index category just two objects with a single morphism between them, we get this diagram,

where the limit syntactically distinguishes it's constituent objects. In Set, it looks like the limit is the set of pairs (x, f(x)), i.e., a function. It's as if the additional f: X -> Y morphism constrains the product set X x Y to the subset where elements are (x, f(x)). Adding more morphisms then constrains the pairs to be (x, f(x) = g(x) = ... = z(x)), for all morphisms f, g, ..., z: X -> Y.

Peter Arndt (Aug 01 2020 at 13:22):

Welcome!
About the shape of the equalizer diagram: The standard notation expresss the same universal property as the cone notation that you wrote down correctly. The

\varphi_Y, \psi_Y

are usually suppressed from the notation because they are equal to

f\circ \varphi_X

(and also to

g \circ \varphi_X

, resp.

f\circ \psi_X

and also

g \circ \psi_X

). So those parts of the cones are not really extra data that you need to carry around in the notation.

Jules Hedges (Aug 01 2020 at 13:25):

Peter Arndt (Aug 01 2020 at 13:27):

Joseph Denman (Aug 07 2020 at 17:46):

@Peter Arndt I meant to say this when I first read your reply, but thanks for your response!

krishnagee (Aug 11 2020 at 14:34):

Hello!! , This is Krisna. I am software system engineer by day - more inclined towards multi-disciplinary system with human centered design in mind. Predominantly, Java/Python and bit of Haskell/Go. Have been reading and enriching myself through - https://golem.ph.utexas.edu/category/ and recent read about https://github.com/hmemcpy/milewski-ctfp-pdf - Category Theory for programmers was quiet fascinating. Exploring the limits and possibilities of self-expressive and self-aware software systems - through semiotics , ACT etc .

Andrey Kurdyumov (Aug 18 2020 at 07:01):

Hi. I'm Andrey and I'm software engineer. Cannot say that I have practical applications at work, more about curiosity what is that and how that can be applied somewhere.

Matt Wilbur (Aug 30 2020 at 13:18):

I am a software developer. However, while the practical side of CT is of course interesting to me, I would like to learn about it from a mathematical point of view as a subject in its own right. My interest in mathematics comes from its own inherent beauty.

However, I only have books and the occasional video to teach myself. I have been told I'm intelligent, but all my more mature mathematics has been self-taught (beyond what I learned in University where I was an Engineering student, which was mostly linear algebra applied to signal processing) and sometimes I get stuck and, admittedly, a little obstinate. I am the proverbial baby learning how to crawl.

Carlos Vera (Sep 01 2020 at 12:48):

Originally a physicist working on quantum optics, moved over to Astrophysics for my PhD, completed a postdoc on the same field, later got a faculty job which I eventually left to work on the healthcare industry. I came in contact with CT a couple of years ago and have been learning on my own ever since. Been through a couple of books, occasional papers and a few vids, which left me with: tons of unanswered questions and no one to help me solve them.

John Baez (Sep 03 2020 at 22:41):

Pedro Minicz (Sep 21 2020 at 00:11):

I am finishing my CS undergraduate degree and already started taking some classes for a mathematics master's degree. I always loved programming languages and last year finally got around to implementing one. This little rabbit hole led me to learn about Haskell, lambda calculus, and type theory. Now I can say I have a new passion for proof assistants, category theory, and type theory. I am still very much a beginner and very enthusiastic about that!

John Baez (Sep 21 2020 at 00:19):

Matteo Capucci (he/him) (Sep 21 2020 at 07:52):

Andrej Bauer (Sep 21 2020 at 08:25):

Hi, I was invited here even though I am not a category theorist. Anyhow, I am very glad to have found the hole that @John Baez is hiding in.

Fintan Halpenny (Sep 21 2020 at 09:22):

Hey :wave: programmer here that got interested in category theory since Haskell is my favourite language to work in. I'm currently getting to grips with it all by going through 7 Sketches of Compositionality.
My dream is to figure out how to think about my work categorically and discover nice solutions to whatever domain I'm thinking about :grinning_face_with_smiling_eyes:

David Michael Roberts (Sep 21 2020 at 11:07):

Matteo Capucci (he/him) (Sep 21 2020 at 11:36):

John Baez (Sep 21 2020 at 15:48):

This is where I talk about category theory... I talk about many other things on my blog Azimuth, and these days I'm talking about nonstandard models of arithmetic on Michael Weiss' blog Diagonal Argument, and other math questions on The n-Category Cafe. Maybe I should make it a bit easier to find everything in one place.

Henry Story (Sep 22 2020 at 14:25):

I thought that if one contributed to the HoTT book, as you did, that one counted as a Category Theorist :-) Is there such a gap? There are conversations here on that topic, such as this one on the HoTT book.

Mike Shulman (Sep 22 2020 at 15:44):

There's also a HoTT zulip, though, where questions about HoTT might find a higher ratio of interested folks. The HoTT book does assume more category theory background than would be ideal, and category theory is a very useful tool in type theory, but the subjects are quite distinct.

Henry Story (Sep 22 2020 at 15:55):

Ah yes, I see the HoTT Zulip is here and Andrei is there. But it is not very active either. Activity is quite important on such forums. It's the only thing that can explain how it is possible for Category Theory to be discussed on Twitter.

Nikolaj Kuntner (Sep 22 2020 at 18:09):

Isn't that easily explained by mathematically inclined programmers being interested in it?
(I remember people getting their knickers in a twist for an array of reason, when some others on twitter where posting about how hard category theory is, along with screenshots of their notes on modular arithmetic and Lagrange's theorem)

সায়ন্তন রায় (Sep 23 2020 at 02:59):

Henry Story (Sep 23 2020 at 04:41):

It is not clear what you are responding to, and so what your 'it' refers to. I'll assume it is the previous post in the "Introduce Yourself!" thread, and in particular the sentence " It's the only thing that can explain how it is possible for Category Theory to be discussed on Twitter."
I think here is is fundamental to understand the network effect, which is a very interesting mathematical principle, about the faster growth in the number of connections on a (telephone,...) network as it adds new nodes, and so the value of the network as a whole. All of silicon valley is built on this. From the internet itself, to the market clout of Microsoft products, to the success of Facebook, etc... It's a mathematical principle they understand and take very seriously. The more users are on a system that is about connections grows, the more value the system gains as a whole, as it is easier to make connections.

Kent Palmer (Sep 24 2020 at 05:31):

André Beuckelmann (Sep 24 2020 at 07:52):

Joel Gustafson (Sep 30 2020 at 18:22):

Hi everyone! I'm an independent researcher at Protocol Labs working on knowledge graphs and decentralized stuff generally. I'm new to CT but am very interested in its relation to RDF and it looks like some people here have been thinking about that too :eyes:

(recently I've been playing around with adapting the algebraic data model from APGs to RDF natively)

Winston Troughton (Sep 30 2020 at 23:13):

My background is in computer science, working as a software engineer nowadays. My interest in programming languages (Swift, Go, Rust atm) and type systems led me to category theory. Hoping that theory and practice can meet together to make software easier to develop.

Hakimi Rashid (Oct 14 2020 at 03:28):

Hello everyone.
I am currently pursuing Phd in neurosciences. Got interested in category theory along the way and have been trying to incorporate it in my research project. Still a beginner.

Prathyush (Oct 28 2020 at 17:37):

I am a designer/developer who turned to category theory after finding a lot of patterns reappearing in different basis in my work. I found out that Category Theory is a great setting to rigorously study patterns in general. To start learning it, I have been looking at various starter materials and collecting the ones I found together to get an understanding for what resources are out there. I put all the great stuff I found together as an annotated bibliography. I am a beginner at this and would love to hear thoughts and feedback from people here on it. This is the repo: https://github.com/prathyvsh/category-theory-resources

It would be lovely if someone can point me to any great resource that I have left out. Also, great to join a focussed platform to discuss about Category Theory and I hope to learn a lot from you all!

John Baez (Oct 28 2020 at 20:02):

You've got a pretty nice list of introductory textbooks on category theory there, @Prathyush.

Prathyush (Oct 28 2020 at 20:47):

Thank you! Your writing (posts, tweets, n-Category discussions) were highly inspirational when getting into CT and putting this reading list together. Thanks for being a beacon and sharing your wealth of knowledge!

John Baez (Oct 28 2020 at 21:16):

Thanks! :blush: I like seeing that Rosetta Stone chart. It sort of summarizes why I fell in love with monoidal categories.

John Baez (Oct 28 2020 at 21:17):

If you want to add another reference, I'd suggest the 3-volume book by Borceaux, Handbook of Categorical Algebra. It's packed with stuff everyone eventually wants to learn if they go far enough in category theory - and despite the title, it's not heavily biased toward "algebra".

Fawzi Hreiki (Oct 28 2020 at 22:25):

Also, in terms of introductory books, I would definitely add Lawvere and Roseburgh’s Sets for Mathematics

Morgan Rogers (he/him) (Oct 29 2020 at 09:34):

The stream #learning: recommendations has lots of potentially useful resources; sharing such resources was the motivation for creating that stream. Have a browse of the topics there, maybe you'll find some good material to add :grinning_face_with_smiling_eyes:

Matteo Capucci (he/him) (Oct 29 2020 at 12:21):

Alan Jeffrey (Oct 29 2020 at 18:11):

Hi everyone! I'm Alan Jeffrey, I've been known to do categorically-minded work every now and then.

John Wiegley (Oct 29 2020 at 20:48):

Hello, my name is John Wiegley, and I like working with Category Theory in Coq mostly, and recently looking at working with agda-categories as well.

Henry Story (Oct 29 2020 at 21:07):

Prathyush (Oct 30 2020 at 07:49):

I have not been sure what introductory book on Set Theory and logic would be appropriate as an intro. I will definitely try lo look this up and evaluate the work.

Nikolaj Kuntner (Oct 30 2020 at 17:40):

@Prathyush I have a similar list of category theory resources here, maybe you find something you haven't included yet

Nikolaj Kuntner (Oct 30 2020 at 17:44):

Yeah I suppose you mostly have recent books (younger than me) and less so on topoi but instead more CS.

Fawzi Hreiki (Oct 30 2020 at 21:03):

Sets for Mathematics is more so category theory (but with a focus on the category of sets) than traditional ZFC-based set theory. If you're looking for a good logic and set theory text, Peter Johnstone has a very slim (approx. 100 pages) book 'Notes on Logic and Set Theory' .

Kale Evans (Nov 12 2020 at 22:22):

Hello all :wave: .
My name is Kale Evans. I am a Software Engineer. Most notably, I've worked at The MathWorks, and currently Spotify. I am very interested in jumping back into theoretical mathematics, principally via Category Theory, and applying it to a host of real world problems. I am also interested in engaging with all of you. Super happy to be here.

Parth Patel (Nov 14 2020 at 12:57):

This is Yaan, as of now i don't really have a proper tag to label my identity, but I'm in final year of my aerospace undergrad, wishing to move either to pure mathematics or theoratical physics in my grad school. Turns out category theory just came by and attracted me, let's see how it goes.

Thank you all beautiful people to build up this community. :purple_heart::blush:

Matteo Capucci (he/him) (Nov 14 2020 at 13:37):

Sacha Ikonicoff (Nov 15 2020 at 21:21):

I am Sacha Ikonicoff, I have finished my PhD last year in Paris, Muriel Livernet was my advisor, and I am starting a postdoc in Calgary with Kristine Bauer. I study algebraic topology and especially algebraic operads, I also studied unstable cohomology and I guess I would be tagged as working in homotopy theory. Category theorist were my prime interlocutor in Paris, and they still are here, so I am glad to be part of this group. :tada:

Eric Forgy (Nov 28 2020 at 22:44):

I sometimes refer to myself as the "jester in the court of kings" being old friends with John Baez and Urs Schreiber going back to the ancient sci.physics.research days (anyone remember that?

) and the early days of the String Coffee Table and the n-Category Cafe.

One of the highlights of my research experience was publishing a preprint with Urs:

back when I was at MIT Lincoln Laboratory (2004). The work resulted from some things I started in my dissertation in computational electromagnetics at the University of Illinois at Urbana-Champaign (2002).

Sadly (as some might say), I sold my soul and went to work in Wall Street in 2005 and have had a long career in financial services since then, but I always tried to keep one foot in research by publishing occasional informal articles on my blog.

As a mathematician, I am certainly a "fool", but when it comes to engineering (science or finance), I think I don't do too bad. I am pretty sure I can claim to be the first person to ever apply noncommutative geometry to mathematical finance :nerd:

Six years ago, I left the corporate world and have been on my own working on various startups with some successes and some (painful) failures. Recently, I decided to get back to my old research bridging higher maths with practical applications and am definitely open to collaboration (so don't hesitate to get in touch).

I am somewhat of an evangelist for the Julia programming language and think it has huge potential for applied category theory. I believe a "killer app" is automatic differentiation a la Conal Elliott and Scientific Machine Learning. I am active on the Julia Zulip where it has been fun to see world's collide with @Evan Patterson and @James Fairbanks attracting a lot of category theorists over due to the awesome work they are doing on Catlab.jl and building up the AlgebraicJulia community..

Matteo Capucci (he/him) (Nov 28 2020 at 23:00):

Non-commutative geometry and finance? Sounds intriguing. Can you expand on that or is it some industry secret?

Eric Forgy (Nov 28 2020 at 23:03):

Matteo Capucci (he/him) (Nov 28 2020 at 23:12):

Eric Forgy (Nov 28 2020 at 23:14):

Alexander Cowtan (Jan 20 2021 at 08:45):

Hey, I'm a PhD student at Oxford. Interested in cats for quantum things: CQM, topological QC, TQFTs etc.

Sasha B (Feb 02 2021 at 06:05):

Oh, I just noticed this thread. Hi everyone! I'm a programmer in Melbourne Australia with no formal education or any real reason to be here, but I like the tiny bit of category theory I know, so I thought I'd join.

John Baez (Feb 02 2021 at 06:52):

Matteo Capucci (he/him) (Feb 02 2021 at 09:20):

Valeria de Paiva (Feb 02 2021 at 19:08):

hi everyone! Yes, I have been around for a while, but I would like to introduce myself, as I have a favour to ask.
I'm Valeria de Paiva, I work in the Topos Institute and I like to use category theory in many different applications. Now I am very keen on making sure that women are not short-changed in their professional lives and I am very much against 'manels', panels with only men on them. So, for the favour, I would like to have a list with women in Category Theory. I would like women here to go to the google doc https://docs.google.com/spreadsheets/d/1lb3zW7Zk-KI0mY0x7dLZ0pHFeLLeobc5itTBrtVBwAo/edit#gid=0 and add themselves to the list. The rules are very simple: no need for a PhD, no need for a(n academic) position, no need for reputation points. anyone who wants to work with category theory and identify as a woman can add their names, please.

Amar Hadzihasanovic (Feb 02 2021 at 20:37):

Hi Valeria, I'd like to forward this to my colleagues, but I cannot access the spreadsheet and get a “You need access” message, is that intended?

Valeria de Paiva (Feb 02 2021 at 21:09):

No Amar, not intended at all. let me check the Google Doc. Thanks for forwarding!

Valeria de Paiva (Feb 02 2021 at 21:11):

Amar Hadzihasanovic (Feb 02 2021 at 21:31):

Valeria de Paiva (Feb 03 2021 at 05:27):

a clarification: I was asked by a friend if he can nominate i.e add the name of a young female category theorist that's a friend/student/colleague.

the reason I'm asking for self-nominations is simply because I won't go around trying to find people. but male allies who know about shy and retiring females (and there are many!), please do add them in. thanks!

Peter Arndt (Feb 03 2021 at 09:00):

Hi @Valeria de Paiva , I am sending this around, but I know enough women who would curse me if I put their data on a Google hosted list, and probably are reluctant to do so themselves. Maybe you could - on that spreadsheet - provide an alternative link or email address for such women.

José Siqueira (Feb 03 2021 at 10:44):

Hi everyone, I'm José Siqueira and I'm in the final months of my PhD in Cambridge, during which I've been working on the categorification of Internal Set Theory (and by extension nonstandard analysis). I didn't realise this page existed! I have to thank Valeria for making me notice it through her recent email to the mailing list. Great to see so many names :)

Amar Hadzihasanovic (Feb 03 2021 at 10:57):

Hi José! Was your work related to Moerdijk and Palmgren's topos approach or is it a different idea? (I guess “categorification” can mean different things...)

José Siqueira (Feb 03 2021 at 11:29):

Hi there! Moerdijk's approach is a bit more semantics based, drawing from NSA directly through the Robinson route in a sense (i.e via the underlying idea of ultrafilter), while Palmgren's constructive NSA uses similar ideas to that of my starting point (E. Nelson's Internal Set Theory). My main inspiration is actually an old paper by A. Kock and C.J. Mikkelsen; my version uses different tools and is a fundamentally different approach, but it all ends up being topos theory in the end.

Valeria de Paiva (Feb 03 2021 at 13:51):

hi @Peter, I first worried about the same. Had an exchange almost ten years ago with Catarina Dutilh Novaes, me saying that there would be Viagra ads all over the list of Women in Logic, she saying we'll worry about it when it does and she was right. We haven't had issues, so far. Women in Programming Languages have their list in GitHub, but the point here is not to make sure category theorists know how to use github, but to make the old excuse that people don't know women doing CT even more lame. (I don't understand it, as I keep having to remove rubbish from even slideshare comments...)

Valeria de Paiva (Feb 03 2021 at 13:56):

hi @José, really glad to hear my message was useful!! good luck with the writing, it's a hard time. sending you good vibes :hug:

José Siqueira (Feb 03 2021 at 23:23):

Marta Bunge (Feb 04 2021 at 00:18):

I noticed that the list of signatories is increasing and includes mathematicians from many different countries - it ought to have some impact!

John Baez (Feb 04 2021 at 00:19):

Marta Bunge (Feb 04 2021 at 00:21):

Valeria de Paiva (Feb 04 2021 at 00:43):

Frederick Kintanar (Feb 08 2021 at 17:01):

I am studying models of lexical semantics as well as broader issues in formal linguistics and cognitive science, with a particular interest in Chu spaces (as discussed for example by Jon Barwise and Jerry Seligman in Information Flow: The Logic of Distributed Systems). I am interested in recent work in Applied Category Theory, including Petri Nets and the semantics of dependent type theories.

Matthias Hutzler (Feb 11 2021 at 20:53):

Hi all, I'm Matthias Hutzler (pronouns: he/him), a PhD student in Augsburg, Germany, planning to finish in a couple of months. I'm working with classifying toposes for geometric theories, in particular I'm trying to find classified theories for some toposes in algebraic geometry.

Matthias Hutzler (Feb 11 2021 at 20:54):

Morgan Rogers (he/him) (Feb 11 2021 at 20:55):

Hi Matthias! Which toposes are you talking about specifically? Always keen to hear more about people working with toposes :grinning_face_with_smiling_eyes:

Matthias Hutzler (Feb 11 2021 at 21:02):

I found a theory for the big infinitesimal topos ("infinitesimally thickened local rings", in the simplest case) in my master's thesis and I think I can do it for the big crystalline topos by now. I might look at pro-étale and prismatic topos in the future.

John Baez (Feb 11 2021 at 21:12):

Neat! By the way, nonexperts will find the idea of a "big infinitesimal topos" paradoxical.

David Michael Roberts (Feb 13 2021 at 09:45):

Hi @Matthias Hutzler where about in Australia? (I guess Sydney, Melbourne or Canberra?)

David Michael Roberts (Feb 13 2021 at 09:47):

Also, I've been waiting for the slow progress on the points of these algebraic geometric toposes, and I say such results are always very cool.

David Michael Roberts (Feb 13 2021 at 09:47):

In case anyone else doesn't know, Matthias' Masters supervisor was Ingo Blechschmidt.

Matthias Hutzler (Feb 13 2021 at 14:10):

Haven't decided on a city / university yet. (Why don't you mention Adelaide?) Or rather, I don't know where I have a chance to get a position.

Matthias Hutzler (Feb 13 2021 at 14:15):

Officially, it was Marc Nieper-Wißkirchen. But yes, Ingo had a huge part in it.

Keith Elliott Peterson (Feb 13 2021 at 20:12):

Hi. I'm just an amateur mathematician. I'm here because Baez nagged me to be here.

John Baez (Feb 13 2021 at 22:07):

David Michael Roberts (Feb 13 2021 at 22:34):

Adelaide doesn't have a category theory group, let alone topos theory. I'm officially employed on a grant looking at K-theory. Danny Stevenson does homotopy theory/oo-categories. Raymond Vozzo is a differential geometer who works on gerbes. And that's the closest we've got. I recommend Adelaide as a city to live in, but getting an academic job is a different matter. Dom Verity or Richard Garner would have a better idea about options for actual CT jobs in Australia.

David Michael Roberts (Feb 13 2021 at 22:37):

But the academic job market in Australia is going to be very rough for a bit. And the fact you won't be able to enter the country until our borders are opened. That's not going to happen in just a couple of months

Matthias Hutzler (Feb 13 2021 at 23:43):

David Michael Roberts (Feb 13 2021 at 23:58):

Sorry I couldn't give you better news! Best of luck with finding a position (I do think it would be cool if you could come to Australia, we don't have any topos theory people here, really, aside from me dabbling a little)

Emilio Minichiello (Feb 20 2021 at 01:13):

Hi everyone, I'm Emilio (he/him), doing a math PhD at the CUNY Graduate Center in New York City studying under Mahmoud Zeinalian, I'm really interested in applications of higher category theory to differential geometry and am hoping to meet others with similar interests.

John Baez (Feb 20 2021 at 01:16):

Hi, @Emilio Minichiello! Say hi to Mahmoud for me sometime. I've met him a couple of times when I spoke at Dennis Sullivan's seminar.

Emilio Minichiello (Feb 20 2021 at 01:18):

TJ Davis (Feb 23 2021 at 01:23):

Hello! I'm a masters student who is working on triangulated categories, specifically on Gorenstein Defect categories.
I want to get into applications of toposes into algebra, but i lack the needed back ground...

Morgan Rogers (he/him) (Feb 23 2021 at 10:03):

Chirantan Mukherjee (Feb 26 2021 at 11:14):

Hi everyone, I am a Master student at the University of Trento, Italy. I will be working on n-fold Segal Spaces for my master thesis under the supervision of Dr. Nima Rasekh in the research lab of Prof. Kathryn Hess at EPFL. I want to puruse my PhD in same direction of homotopy theory/category theory.

Amar Hadzihasanovic (Feb 26 2021 at 12:05):

Chirantan Mukherjee (Feb 26 2021 at 12:11):

Unfortunately not. I have to look in the north of EU or US for a PhD for that reason

Matteo Capucci (he/him) (Feb 26 2021 at 12:13):

I originally aimed at Trento for my master, until I asked whether it's a good choice for people wanting to pursue a career in CT, to which they replied 'not even remotely'. That's why I went to Padua.

Matteo Capucci (he/him) (Feb 26 2021 at 12:14):

(Hi Chirantan! I have a few friends up there in Trento anyway, they probably study with you)

Chirantan Mukherjee (Feb 26 2021 at 12:21):

Oh wow. I got interested in the CT last year during fall. I chose Trento because of their active research in geometry. Alas! they are not that active in topics related to AT

joaogui1 (he/him) (Mar 01 2021 at 09:16):

Hi folks! I'm João, a Brazilian Undergraduate Student in Computer Science. I believe I've been interested in Category Theory for the last 7-8 years, but now with the pandemic I've finally decided to take the plunge and learn it seriously, nice meeting you all :D

Matteo Capucci (he/him) (Mar 01 2021 at 09:28):

joaogui1 (he/him) (Mar 01 2021 at 09:36):

Matteo Capucci (he/him) (Mar 01 2021 at 09:39):

Matteo Capucci (he/him) (Mar 01 2021 at 09:40):

Daniela (Mar 08 2021 at 14:23):

HI everyone !
I am Daniela CIALFI, a cognitive-behavioural economist, a postdoctoral researcher at the University of CHIETI-PESCARA (ITALY) and former visiting postdoc at Simons Institute for the Theory of the Computing (UC Berkeley).

John Baez (Mar 08 2021 at 15:17):

Hi! What sort of projects are you working on? A blend of cognitive-behavioral economics and computer science?

Matteo Capucci (he/him) (Mar 08 2021 at 16:53):

Jules Hedges (Mar 08 2021 at 18:42):

Hi! Cool, I think we don't have many economists on here... I'd be very curious to hear what brings you to category theory as a behavioural economist

Graham Manuell (Mar 15 2021 at 12:35):

Hello everyone! I'm a postdoc at the University of Coimbra working mainly in pointfree topology.

Morgan Rogers (he/him) (Mar 15 2021 at 12:55):

Sahil Imtiyaz (Mar 16 2021 at 14:12):

Hi everyone! I am in last year of my PhD. I am working on topology of contextuality and non-locality and its interpretation in interactive model of computation.

Manuel Baltieri (Apr 19 2021 at 03:06):

When it comes to categories, I'm only just starting, but thanks to people like @Nathaniel Virgo (who so kindly introduced me to CT and this community) I feel like this may lead me into some really cool topics + ideas. 'Normally', I'm working somewhere between theoretical neuroscience and AI. But also theoretical biology, control theory + inference/filtering + information theory, etc.

I have a keen interest for cross-disciplinary approaches (to any kind of problem really), and for common topics that seem to appear in different fields (it all started with the duality of inference and control, Kalman and many others after him). This is probably the main reason I thought CT would be of great help: what are the fundamental components of all these things that I like and that seem to pop up in apparently unrelated fields?

To give a few key words that might help place me (but don't make me an expert on):

It is quite likely I'll spend some time just lurking for now, especially in the streams (with questions) for beginners, but in the meantime, nice to meet you all!

John Baez (Apr 19 2021 at 15:14):

Those are great topics you're studying, @Manuel Baltieri. Using category theory to help clarify these will be a big job, but ultimately should be really interesting.

Manuel Baltieri (Apr 19 2021 at 15:40):

I'd be lying if I said your work on categories for control wasn't a good way to get me into CT, so thank you (and thanks to Nathaniel, who once again brought this out with me)!

Spencer Breiner (Apr 19 2021 at 15:41):

Hi @Manuel Baltieri. There are a bunch of people around here interested in those kinds of topics. The most directly relevant, if you haven't already seen it, is @Toby Smithe's presentation from the MIT seminar or ACT (and the associated paper). There is also this youtube channel with some talks in this vein by others that like to hang out here.

Toby Smithe (Apr 19 2021 at 15:59):

Hey, @Spencer Breiner and @Manuel Baltieri. First of all, welcome @Manuel Baltieri, and thanks @Spencer Breiner for @ing me: I find this place quite overwhelming so only log in occasionally. I should say that my ACT talk is somewhat troublesome and I've been working on cleaning it up quite significantly. I've now got quite a general scheme for describing the structure of active inference systems as an indexed functor from an indexed category of statistical games (describing the statistical part) over polynomials into an indexed category of dynamical systems (of various kinds), also over polynomials. I don't like to announce things before I'm feeling secure in them, so I haven't said much recently. But I gave a talk sketching some of this material recently, and the slides are at https://tsmithe.net/papers/20210317-cgt-talk.pdf -- that talk didn't cover much of the "active" part of "active inference" (which is where the polynomials come in), and I'm writing that up at the moment. I also believe that, in 'nice' cases, the indexed functor I mentioned should have a right adjoint which associates to a dynamical system a "canonical statistical game", but I haven't finished working the details of that part out.

Jules Hedges (Apr 19 2021 at 16:08):

I can say hi too - I'm thinking about many of these topics too, plus I'm behind the youtube channel that Spencer linked (together with @Philipp Zahn)

Jules Hedges (Apr 19 2021 at 16:08):

Joe Brucker (Apr 20 2021 at 18:36):

Hi! I’m Joe Brucker and I do NLP research with the Lexical Grounding team @ harvard. Before that I worked in Semantic Web; before that, Data Science; before that, on both sides of securities trading in emerging market derivatives (both algo and traditional - over the phone on a desk) if anyone wants to talk about macro-econ or trading decision making.

I got interested in Category Theory by a NeurIPS paper on Natural Graph Networks, and my interest was buttressed by the unique thought processes and undeservedly warm welcomes of Bruno Gavranovic+Elias Judin, and a super interesting discussion I got to attend of the latter 2 plus Bob Coecke + Brendan Fong on Clubhouse.

I’m interested in research in category theory + semantics if anyone is looking for a grunt/collaborator. I know very little, but I have a hunch that there are a lot of useful applications in FrameNet, PropBank, and the work done in Ontology development by Martha Palmer at CU Boulder.

Edit: I’m also actively looking for research and doctoral positions, and am eligible for citizenship/work in Israel, Germany, Argentina, and the US!

Valeria de Paiva (Apr 20 2021 at 19:36):

hi Joe, nice to meet you! I have done (and I'm still doing) some work with Martha Palmer (we have one paper under review now, a continuation of (Kalouli, A.-L., Buis, A., Real, L., Palmer, M., de Paiva, V.. Explaining Simple Natural Language Inference. Proceedings of the 13th Linguistic Annotation Workshop (LAW 2019), 01 August 2019. ACL 2019, Florence, Italy. ) So super-stoked by your message.

Fabrizio Genovese (Apr 21 2021 at 01:17):

Me, @fosco and @Daniele Palombi have been having this idea in mind of characterizing some constructions of Technical Analysis categorically

Fabrizio Genovese (Apr 21 2021 at 01:21):

We worked on it a bit, but not much (it's difficult to really think about abstract trading theory in such a bull market!). In any case, the idea is simple: An asset pair is a continuous function on

\mathbb{R}^+

. You only see a part of it, say an interval

[0,x]

for some

x

. The goal of a trader is to give a guess of how the function will evolve in the future. Clearly stated in this way it is an impossible task, because you can prolong this continuous functions in any way you wish. But the trader makes the assumption that:

Fabrizio Genovese (Apr 21 2021 at 01:21):

For this reason, traders devote a huge amount of time to develop tools that can extract/summarize information from a price graph.

Fabrizio Genovese (Apr 21 2021 at 01:22):

This includes using candlesticks, EMAs, RSIs, Volume indicators, you name it. All these constructions can be described neatly in categorical terms. Also, categorifying all this is the best way to come up with general techniques to make new tools available :smile:

Fabrizio Genovese (Apr 21 2021 at 01:25):

The _very_ funny thing about trading (that usually makes physicists/dynamical systems people go galaxy brain) is that they work as self fulfilling prophecies: The "dynamical system" at play is just the resultant of the single choices of all traders. So, if, say, everyone uses EMA indicators to make decisions, this choice itself will end up influencing the price, making the EMA indicator being predictive in some sense

Fabrizio Genovese (Apr 21 2021 at 01:27):

for instance, make the unreasonable assumption that everyone starts selling when the daily graph crosses the EMA200 from above. That being the case, said event will inevitably push the price further down. So, detecting this crossing becomes an effective indicator for trend inversion. Clearly the reason why this often does not work in practice is because different traders use different strategies, indicators etc. So you need to properly understand market sentiment to be able to read indicators correctly. :smile:

fosco (Apr 21 2021 at 05:19):

Hi! Fabrizio said a lot; I can add a few details on the mathematics if you want :-) let's discuss!

Joe Brucker (Apr 29 2021 at 00:33):

@fosco @Fabrizio Genovese @Daniele Palombi
I'd love to chat! My first startup was a little prop fund that used RSI really heavily, this is really interesting stuff!

You're :a: bsolutely right that traders spend a ton of time setting up their trading systems - it's why everyone is still stuck in VBA and MS Excel :(
Categorifying these indicators is a really interesting idea for tool development! IIRC, the black-scholes model is basically a re-wording of some model from physics, so making the ideas more transferrable like you're describing sounds like it has a lot of upside!

When you say untractable, do you mean that it's tough for any one individual trader to move the price? There are also a few different environments (OTC markets, periods of illiquidity, interbank traders) that the price can move from buying large chunks of stock or from the seller discriminating based on who's buying. Offline, I can tell you how some traders get around this haha.

I'm also thinking it could also be modeled as discrete, would that make it easier? At an operational level, and depending on the asset/exchange/flow, the price may have artificial 'ceilings' and 'floors' from the limit orders and exchange halting.

The inter-asset/intra-asset self-fulfilling prophecies are all too real, I can still feel the stress of stop-loss slippage. It's really interesting to think of all these price changes as just buy/sell volume proportion at different intervals of time

Joe Brucker (Apr 29 2021 at 00:42):

Hi Valeria, nice to meet you too! And oh wow! I was just reading your paper on annotations in the SICK corpus- I'm working on an annotation tool for coreference - I'd love to hear how you think about grounding/explicitation of referents for inference, and your work on entailment! Would it be O.K. if I emailed you?

Joe Brucker (Apr 29 2021 at 00:43):

Also! is there a section here for CT+NLP? Would love to hop in but I haven't seen it yet

Joe Moeller (Apr 29 2021 at 02:09):

There should be a section for NLP. Maybe it fits in another stream though. Anybody have any thoughts where it would best fit?

John Baez (Apr 29 2021 at 02:14):

A conversation in #practice: applied ct is probably fine for now, until there's enough conversation to warrant a whole stream.

John Baez (Apr 29 2021 at 02:20):

We have a stream called #practice: neuroscience that hasn't seen any conversations since December. It's probably not good to be too quick to set up streams before we even know that people will seriously use them. Conversations within a stream are perfect for when you don't know how much you'll be talking.

Valeria de Paiva (Apr 29 2021 at 02:35):

hi @Joe Brucker , we actually have 3 papers on SICK( one on entailments, the one in contradictions you're reading and one about "one-word-apart" pairs of sentences in SICK). I thought in 2016 that SICK would be an easy place to test the new neural nets emerging from Google at that time, the Parsey McParseface times. but we're still working on it 4 years later! oh well.

Katerina and I have these nice demos for our work: GKR Demo--
http://lap0973.sprachwiss.uni-konstanz.de:8080/sem.mapper/ describes our KR system, while Hy-NLI Demo-- http://lap0973.sprachwiss.uni-konstanz.de:8081/gnli/hynli.jsp-- is an overview of our hybrid--neural and symbolic-- inference system, if you're interested. Katerina just defended her PhD in Konstanz. So to your question, we don't ground things explicitly, we use WordNet and a generic ontology SUMO for our concepts. and sure, please email, I'd love to chat more.

Fabrizio Genovese (Apr 29 2021 at 09:07):

No, by "untractable" I mean that this supposed dynamical system depends on a huge number of variables, basically on all the moves and internal belief system of any trader out there. So it's not something that can be reasonably simulated or analyzed. The best thing you can hope to do is to define some metrics that, for some reason, give approximate predictions for this system

Fabrizio Genovese (Apr 29 2021 at 09:11):

Obviously since things change all the time, some metrics may be predictive in some interval/timeframe, and some may not. The example you make with the RSI is indicative: If you look at markets in crypto on the short timeframes, the RSI is often quite predictive. If you look at the monthly candles of ETH the RSI basically pierces the screen and goes up and up and up weeeeell beyond what any rational human being would consider a reasonable level to buy lol

Fabrizio Genovese (Apr 29 2021 at 09:12):

In any case I'd like to chat, working with someone that knows TA well enough could come in handy! There's only this problem of having negative free time at the moment. Hopefully when a few deadlines pass it will get easier.

Bruno Gavranović (May 02 2021 at 13:46):

I'm a bit late to the party, but hi @Joe Brucker! And welcome! It's great to have you here.

ww (May 04 2021 at 18:20):

Hi! My name is William Waites. I belatedly realised that there was an "Introduce Yourself" topic here. I work on things like graph rewriting for studying biological systems -- currently epidemics at LSHTM for somewhat obvious reasons, but previously things like synthetic genetic circuits and vertex models of epithelial tissues (sheets of cells one cell thick). In the more distant past I also did telecommunications engineering and also some semantic web stuff. Despite having been exposed to CT for many years, it's only recently started to sink in and I find that I understand what I have been doing a lot better now. I'm really interested in trying to more systematically bring the insights from the CT understanding of composable open systems to the kind of modelling work that happens in biology and population health. Nice to meet you all!

ww (May 04 2021 at 18:23):

Chad Nester (May 04 2021 at 21:00):

Tim Campion (May 04 2021 at 21:16):

Hi! My name is Tim Campion. I am a 6th year PhD student of Chris Schommer-Pries at the University of Notre Dame. In the fall I will start a postdoc with Emily Riehl at Johns Hopkins University. I am also a moderator at MathOverflow.

I would describe myself as a category theorist at heart who likes to dabble in other mathematical fields while secretly (or not-so-secretly) pretending that they are all category theory. I am particularly interested in

\infty

-categories and homotopy theory (which have become roughly synonymous for me). With others, I have done work in cubical homotopy theory, and also work attempting to apply the techniques of categorical homotopy theory to classical model theory.

Between some familiar faces I haven't seen in awhile and unfamiliar faces, I'd like to get to know the folks here better. DM me your favorite universal property!

Ivan Di Liberti (May 04 2021 at 21:55):

John Baez (May 04 2021 at 22:55):

Hi! As you know, I really hope to work with you and @Evan Patterson and @James Fairbanks and @Owen Lynch and others on compositional models of infectious disease. I won't be able to do serious work on this until the end of June, but I'd be happy to brainstorm ideas here now.

Leopold Schlicht (May 06 2021 at 14:33):

Hi! I'm a 3rd year undergraduate interested in category theory and foundations of mathematics. Currently I'm also studying functional analysis and complex analysis for my degree course. Seems like I found a really cool place here. :-)

José Siqueira (May 06 2021 at 15:33):

Francesco Genovese (May 07 2021 at 09:29):

Fabrizio Genovese (May 07 2021 at 09:37):

Amar Hadzihasanovic (May 07 2021 at 10:02):

Tim Hosgood (May 07 2021 at 13:29):

Hi @Francesco Genovese ! your work on twisted sheaves of perfect complexes seems really interesting to me (I work with twisted cochains, which i guess must be somehow equivalent, since they also give a dg-enhancement!)

ww (May 07 2021 at 14:36):

I hope so too! I'll start a thread or two over the next days with some ideas that have been percolating. I've had had my head down for various reasons the past while but can lift it up again now. Also just saw @James Fairbanks give an excellent talk about the Aglebraic Julia at the GReTA seminar which was very nice!

Francesco Genovese (May 07 2021 at 18:54):

hi! actually they are just dg-enhancements of derived categories of twisted sheaves and it's a work in progress - hopefully out before the end of this academic year! In any case, I still at least a bit familiar with twisted complexes of objects in dg-categories, there is another work which explores them as a possible variant of projective or injective resolutions

Todd Trimble (May 17 2021 at 21:34):

Tim is very active at MathOverflow where we've interacted to some extent, and now he's a newly elected moderator!!

Ivan Di Liberti (May 17 2021 at 21:44):

Frederick Kintanar (May 26 2021 at 23:12):

I am not familiar with this team, but since I have an active interest in lexical semantics, perhaps I should know more. Could you provide some links to relevant papers or web pages?

Henry Story (May 27 2021 at 07:57):

Hi @Joe Brucker , @ww nice to see others with semantic web past here. (We also have @Eric Neumann lurking here and I am sure a few others).
I have been working on the Semantic Web since 2004 and got to see the value of Category Theory by using it programming in Scala starting around 2011. Somehow around 2016 I ended up taking 4 years off on a (self-financed) PhD which allowed me to study CT deeply, but then ran out of money. Luckily I received funding this year from the EU to work on a project called "Solid Control" where I am writing a Read-Write access controlled web server Reactive Solid. This is allowing me to learning by doing, as I try to apply the concepts I read about. (But it is taking a lot of time, as it is milestone based and I set some slightly too ambitious milestones :grimacing: )
There is a discussion thread Web Cats, for discussion on Web and Category theory related topics.

Jon Awbrey (May 28 2021 at 14:34):

Eric Neumann (May 29 2021 at 15:03):

Hi everyone - Just want to introduce myself. As @Henry Story mentioned, I had been involved early on with the Semantic Web, focusing on data challenges in HealthCare and Life Sciences (HCLS), an area that has continued to grow and now finds biotechs awash with complex data and ontologies exhaustion. More recently, I have been interacting with @David Spivak on applying CT to areas of biomedicine, to go beyond just data models and try to build some foundations for logic and inference in biosystem models. I also plan to participate on Web Cats with interest in working on a Comonad definition for the Web.

Karthik Ravikanti (May 30 2021 at 05:05):

Hi, I'm an Indian software engineer working in Singapore who wants to eventually learn to see categories.

Mehmet Akif Erdal (May 30 2021 at 09:21):

Zhen Lin Low (May 30 2021 at 13:34):

Hello. My name is Zhen Lin Low. I studied category theory at Cambridge and obtained my PhD in 2016. I have been out of academia since then, but it turns out one can never really stop being a mathematician. My research interests include topos theory, categorical logic, and abstract homotopy theory. It seems everything has gone remote/virtual over the last year or so – perhaps I should go to a virtual conference and try to catch up with everyone!

John Baez (May 30 2021 at 15:09):

Leopold Schlicht (May 30 2021 at 15:12):

@Zhen Lin Low Hi! Just out of curiosity: what are you doing outside of academia?

Zhen Lin Low (May 30 2021 at 15:56):

@Leopold Schlicht I was a software engineer then data scientist for a while, but I just quit that job and am thinking about my next steps now.

Mehmet Akif Erdal (May 30 2021 at 20:08):

@John Baez Hello :) I am in Istanbul, Turkey. I finished my PhD in 2017 and currently I am in a position between Lecturer and Asst.Prof.

Morgan Rogers (he/him) (May 30 2021 at 20:20):

ebigram (Jun 05 2021 at 07:57):

Hello, while formally my MS is in ML/NLP, I've been a functional programmer for over a decade and hoping to deepen my understanding around some of its theoretical underpinnings. Of course I've enjoyed reading and watching John Baez, and especially influenced by his nuanced take on applying category theory to learning. I will likely lurk here mostly because much of this stuff is still over my head :]

Fabrizio Genovese (Jun 05 2021 at 17:40):

John Baez (Jun 05 2021 at 17:50):

ebigram (Jun 05 2021 at 18:13):

@John Baez it's not every day where I have an "Annie Hall" moment with the professor himself right here to disabuse me of my wild misconceptions. So as to not invoke a "you know nothing of my work" moment, how would you characterize the research that has been done so far on a CT interpretation of learning theory? IIRC you were equivocal/skeptical about it, but then there were a few publication that made a convincing case for it (I will move this somewhere else, sorry didn't mean to take up room here).

Notification Bot (Jun 08 2021 at 14:09):

Gurkenglas (Jun 11 2021 at 12:16):

Hi. I first learned of CT through Haskell. For years my MO has been to read an nlab page, not get it, and months later there's a level-up chime. When I encounter a confusing mathematical object I try to write down all the morphisms I can find, then see if the diagram has a name. I was sent here to ramble as I search for CT foundations for Scott Garrabant's talk on finite factored sets.

Josh Lalonde (Jun 11 2021 at 20:21):

Hello all, I'm an interested but still rather confused amateur. My background is in philosophy and linguistics, but I've recently started in computer programming. I'll mostly just be lurking as I try to get my head around category theory. I found out about this forum via John Baez's talk at the Categories and Companions Symposium the other day and the Topos Institute website.

John Baez (Jun 12 2021 at 01:38):

Paolo Scarpat (Jul 14 2021 at 21:49):

Hi! I'm Paolo. I graduated in Maths from University of Pavia, Italy, some (many, actually) years ago. Since then I have been teaching Maths and Physics in high school. I'm interested in algebra and number theory, and I'm trying to learn something more about category theory.

Patrick Nicodemus (Jul 24 2021 at 15:12):

Hi folks. My name is Patrick Nicodemus. I am a PhD student in mathematical logic at the university of Wisconsin-Madison. I am most interested in categorical logic and type theory, and simplicial methods in homological algebra.

Valeria de Paiva (Jul 24 2021 at 15:49):

Tim Hosgood (Jul 25 2021 at 00:31):

I'm super interested in simplicial methods in homological algebra, and now I'm wondering if it relates at all to categorical logic and type theory? or are these two distinct interests?

Patrick Nicodemus (Jul 25 2021 at 07:45):

I have the same question. I started studying simplicial methods in homological algebra because monads are a basic structure in computer science logic and categorical semantics, and I wanted to learn about their history and how they originated. So I went back and read a bunch of the early work on this stuff - Godement's book on sheaf cohomology where he shows that you can use simplicial sheaves constructed by the bar resolution of a monad to give simplicial formulas in sheaf cohomology for the cup product/cross product/Steenrod squares, Barr and Beck's work on acyclic models and homological algebra with respect to a monad, stuff like that. It does seem that wherever you have monads you should be able to define some of the basic concepts of simplicial homotopy theory or cohomology, and I am wondering whether it's possible to give an interpretation of these cohomology groups or homotopy groups in the context of the monads arising in computer science logic or formal semantics (an interpretation that would be interesting to computer scientists, I mean.)

I'll mention one specific example of a monad I'm interested in. In Bart Jacobs' book on categorical logic and type theory he gives a very interesting argument that basically all the higher level notions of logic (quantification, equality, logical operators) are ultimately determined by the structural rules of weakening and contraction through some adjunctions related to them. These weakening and contraction operations fit together into a comonad in the category of propositions; this comonad is kind of the logical backbone of the category, as all of the other features of the logic are necessarily determined by it. I would be interested in whether you can define homotopy groups with respect to this comonad which are interesting.

I also want to point out that topos theory has been very influential in categorical logic and type theory, and this also originated in sheaf cohomology theory. It seems like more than a coincidence that both monads and topoi originated in sheaf cohomology specifically and jumped to computer science logic. Surely there is more going on here than the mere coincidence of the same formal structures appearing in both disciplines.

More recently I've begun to think that a lot of the constructions of simplicial homotopy theory or simplicial methods in homological algebra are best understood in terms of monoidal category theory, as the category of simplicial sets is the free cocomplete monoidal category with distinguished monoid, and the category of simplicial Abelian groups is something similar but with Ab-enriched dropped in appropriately throughout, so I have been trying to work out to my own satisfaction sufficiently "monoidal" derivations of many basic notions of simplicial homological algbera.

Henry Story (Jul 25 2021 at 08:07):

Very interesting research @Patrick Nicodemus . Thanks for making those connections. I hope I'll get time to follow up on those some time.
Regarding simplicial sets and computing I found the paper "On the Geometry of inutionisic S4 proofs" by Goubault which looks at the geometry of programs, and a later paper (nearly 20 years later) on simplicial sets and epistemology which is easier to read. links here.

Tim Hosgood (Jul 25 2021 at 14:22):

@Patrick Nicodemus this incredibly interesting to me! my research is all about simplicial methods in geometry, so it’s really interesting to hear about what this sort of stuff might mean in other settings

Tim Hosgood (Jul 25 2021 at 14:23):

Patrick Nicodemus (Jul 25 2021 at 23:25):

I'm happy with what I've been able to figure out so far but I'm not really tied into any community or familiar with the literature so I have no idea how much of what I've been coming up with is new or novel. I'd be happy to talk about it in more detail for this reason so I can understand the relationship between what I've been doing and the existing literature. Hopefully all this isn't known or out of vogue. But I'll give you an example. Recently I came up with what I think is a satisfactory a priori account of what chain complexes are and why they exist. Given any simplicial set, we can interpret this as a formal schema for gluing together copies of a given monoid in a category and its higher tensor powers, the usual geometric realization of this is the special case where the monoidal product on Top is taken to be the join, and the distinguished monoid is the singleton space. In my opinion this gives a very good motivation for what simplicial sets "are" because for any cocomplete monoidal category C with distinguished monoid M there is a unique cocontinuous strong monoidal functor from SSet to C sending the n-simplex to M^{n+1} and preserving the unit and multiplication maps of the monoid. (Here the monoidal product on SSet is Day convolution.) Now we can characterize SAb the same way, if we say that the category C should be Ab-enriched, and tensored over Ab, say that the tensor product Ab\otimes C -> C is cocontinuous in both variables. So given any simplicial Abelian group X, there is a "geometric realization" of X with respect to the monoid M, computed by a coend \int^{n\in \Delta} X_n\otimes M^{n+1}, which tells how to glue together M and its higher tensor powers according to the face and degeneracy maps of X. It turns out that if you simply sit down and compute this coend, all the degeneracies of X dissolve and you are left with the Moore normalization of X. Similarly the cosimplicial object n \mapsto M^{n+1} has a dual kind of Moore normalization M' which is a cochain complex in C, and the original coend simplifies to \int^n N(X)_n \otimes M'_n.
So, by purely computational motivations, i.e. trying to compute the "realization" of a simplicial Abelian group, we are naturally led to replace it by its Moore normalization, and this can give some a priori justification for the notion of chain complex (it is a reduction of a simplicial Abelian group which suffices for the purpose of gluing together monoids in additive categories and their higher tensor powers)

Spencer Breiner (Jul 28 2021 at 15:07):

You can write

\LaTeX

on zulip by enclosing your math in double dollar signs $$M^{n+1}$$

\mapsto M^{n+1}

Martin Brandenburg (Aug 30 2021 at 19:45):

Hi, I am Martin. Some people probably already know me from my posts (sometimes I also find them via a google search and try to understand what I wrote back in, say, 2013), but anyway here is a short introduction followed by some questions.
I am from Germany and finished my PhD in 2014 on the interplay between algebraic geometry and category theory. Similar to Zhen Lin (from whom I learned a lot!) above, I am outside of academia since then and do lots of other stuff (activism, drumming, programming, ...), but cannot really let go of math and in particular category theory.
Now my questions (if they belong to a different stream, let me know): What is the purpose of this zulip workspace? Where can I read something about its development? In which case (and this is sort of my main question!) would you prefer to ask a question here and not on mathoverflow or stackexchange and also not use the category theory mailing list? To be honest, I find the layout of zulip incredibly confusing and the structure unnecessarily complicated, and for this reason I am not really active here. But someone told me to be there and of course I am curious where all of you are hanging out. As you see, I am still trying to figure out what this is all about.

Joe Moeller (Aug 30 2021 at 19:49):

I believe most people find zulip's interface confusing at first, and get used to it if they manage to stick it out.

Joe Moeller (Aug 30 2021 at 19:51):

I don't know if it's written elsewhere, but this Zulip server was started by @Christian Williams sometime last year mostly as a response to the pandemic. The purpose is very general.

Joe Moeller (Aug 30 2021 at 19:53):

There are streams for people to discuss specific topics, connections of CT to other branches of math and science, a general questions stream... people often start new streams to go along with a conference, so people can ask questions and discuss in a more permanent way than zoom chat. I also suspect a lot of the activity that happens here is in the form of private group chats.

Joe Moeller (Aug 30 2021 at 19:57):

I think a description of the structure of Zulip has been written out a few times, but I couldn't point you to it. The top layer is "streams", these are like broad umbrella topics. Inside a stream are many "topics" that are more like specific conversations. Admins and maybe other people can rearrange these if necessary, so it's not a big deal if you start talking about something in the wrong place. You have to seek out and subscribe to streams.

Joe Moeller (Aug 30 2021 at 20:01):

Exactly which messages are displayed is uh, easily manipulated. So "all messages" will put everything you're subscribed to in chronological order. You can make it so you only see the messages in a stream, in a topic, in private messages, or just pms with one person, or one group chat.

Joe Moeller (Aug 30 2021 at 20:03):

You can subscribe or unsubscribe from any stream. You can remain subscribed, but mute a stream, if you want to be able to see it, but you don't want it flooding your notifications. You can mute specific topics if it's boring to you. Am I forgetting anything?

Joe Moeller (Aug 30 2021 at 20:06):

When you go to a stream or topic, and go to type, the list of names on the right will highlight only the people who are subscribed to that stream, the people who can see your message. For example, very few people are currently subscribed to #conference: CT20->21, and I'm taking this as an opportunity to suggest everyone go subscribe to that!

Henry Story (Aug 30 2021 at 20:09):

I guess you would go to StackExchange if your have a well defined question. They tend to shut questions down if those don't fit into a specific pattern, and they don't necessarily have that much humour. But there is a math jokes channel here, though it needs a bit of reviving :-)
So I think there is a space where you need more dialogue to get to understand a question than is afforded by SE, which is also very good.

Mike Shulman (Aug 30 2021 at 22:00):

As for why to go here rather than to a mailing list, my own answer is that "it seems to be what everyone else has done". I don't know why they did it; maybe they also did it just because it was what everyone else did. But once everyone is here rather than on a mailing list, you have to come here if you want to talk to them. (-:

Mike Shulman (Aug 30 2021 at 22:02):

I guess one slight advantage of zulip over a mailing list is that you can choose which streams to subscribe to, and you can mute particular topics. So if there's a long conversation going on that I'm not interested in, I can unsubscribe from that stream or mute that topic and I'll stop getting notified about it.

Mike Shulman (Aug 30 2021 at 22:02):

Henry Story (Aug 30 2021 at 22:03):

I was just typing this: It is very difficult to get latex maths to work well on mailing lists. Zulip has very good support for it - much better than Discord or other channels, which is also I think why there is a zulip HoTT, Lean and Agda.

Conor McBride (Aug 30 2021 at 22:47):

On forums like this, stuff arrives pre-filed. That's huge. My email inbox is pandemonium.

John Baez (Aug 31 2021 at 01:52):

Instead of answering the question you just asked, I'll list a bunch of things people do here that you can't do on MathOverflow or Stackexchange:

John Baez (Aug 31 2021 at 01:53):

In short, it's more of a "category theory community" than those other two websites could ever be, and also (for subtler reasons) more of a community than the category theory mailing list currently is.

John Baez (Aug 31 2021 at 01:58):

In some ways it reminds me more of the old "usenet newsgroups", where people start discussions on many different topics. But those just had "threads" while this has a 2-layer hierarchy: "streams", each with many "topics".

John Baez (Aug 31 2021 at 01:59):

If you find it confusing, you're probably worrying about it too much. It's just people talking. That's always somewhat confusing, of course. But people seem to manage okay, and the good news is that people don't fight very much here.

James Deikun (Sep 09 2021 at 22:25):

Hi, I'm James Deikun, a tech industry person who loves math and used to attend the Category Theory seminar and reading groups at CUNY before COVID. I first got interested in categories because of This Week's Finds and have continued to be fascinated since then, learning and engaging in the occasional lightweight research, especially on optics.

John Baez (Sep 09 2021 at 23:29):

Henry Story (Sep 12 2021 at 13:34):

There's quite a lot of talk on Optics around here recently, from practical ones how to build a web server, to their relation to polynomials, and more... use the search box at the top to find out.

James Deikun (Sep 12 2021 at 15:50):

Sean Gloumeau (Sep 13 2021 at 21:29):

Hello all, I'm Sean Gloumeau from Barbados! I graduated from MIT in May of 2020 in AeroAstro focusing on controls, real-time systems, telecommunications and am just about to get started on an Erasmus Mundus Joint Masters Degree in Embedded Computing Systems. Even though I absolutely love math, a calculus proof-based math class broke my spirit in my first year as an undergrad, so I decided to pursue it more as a hobby since then. Now that I'm getting into research I really want to marry math into my papers, and Category Theory has caught my eye. I really love reading Tai-Danae's pieces (including topology from a CT perspective which I'm very excited to read in its entirety), and looking into the Fong-Spivak applied CT books and lectures on YouTube. Since I have a year before I choose a research topic, my main goal is to learn as much CT, and as many examples of application, as I can! I believe lurking and interacting with others on this zulip will aid me quite a lot, so thank you all for having me :smile:!

Hart Montgomery (Sep 14 2021 at 19:34):

Hi Everyone, I'm Hart Montgomery from San Francisco, CA. I'm a research scientist in cryptography at Fujitsu. I've become interested in category theory through a pretty circuitous route: over the past few years, I (with some wonderful, very smart coauthors) have written some papers connecting public-key cryptography (and more powerful cryptographic primitives, like fully homomorphic encryption if you know what that is) with mathematically structured simple primitives (i.e. one-way functions or pseudorandom functions, and again, apologies for the cryptographic terms). It seems like mathematically structured computational hardness assumptions are required in order to build certain cryptographic primitives (and in some cases, we can prove this explicitly, although we would obviously like to be able to prove more powerful statements in this regard). However, sometime last year, we (myself and others working on these problems) realized that we didn't have strong enough tools for handling the mathematical structure in the types of proofs we wanted to write about this, and thus needed to learn category theory. So here I am!

If anyone is interested in "computational category theory," I'd love to hear your thoughts, and please feel free to reach out. Thank you all very much for your time, and I'm looking forward to learning from this community. Thanks again!

John Baez (Sep 14 2021 at 19:38):

Hi! You might be interested in @dusko's work on category theory, computation, and computer security.

Fabrizio Genovese (Sep 14 2021 at 19:45):

Computational category theory, as in "talking about computation and even more importantly complexity" is still quite underdeveloped I'd say, but it is definitely something the community should work on. I'm always happy when someone does something going in this direction!

Fabrizio Genovese (Sep 14 2021 at 19:46):

Personally I used category theory to link ZK-SNARKS and finite state machines, but nothing more than this.

Hart Montgomery (Sep 14 2021 at 20:41):

Thanks for the advice! I have actually come across his work before; his website is one of the first to come up when you google "computational category theory."

John Baez (Sep 14 2021 at 21:30):

Hart Montgomery (Sep 14 2021 at 21:52):

Thanks for the kind words! I took a quick look at your paper. It looks interesting, but I haven't had time to go through the details. In the intro, you say, "To do this, we bypass the problem of modelling cryptographical primitives categorically..." which is what we have basically tried to do. Our formulations are probably pretty appalling to properly trained mathematicians though--some of this is due to the difficulty of modelling computational primitives, and much of it is probably due to our inexperience and lack of knowledge of category theory. If you're interested, I can share a manuscript, although I'll need to check with my coauthors first.

Fabrizio Genovese (Sep 15 2021 at 12:47):

Hehe, we took the approach we took exactly because there wasn't much developed already in the direction of cryptographic primitives done categorically, so we took advantage of the fact that zk-SNARKS can be obtained from boolean/arithmetic circuits with already developed techniques, and we focused on circuits instead.

I'll be happy to read the manuscript if you share it, but I do not have too much time at the moment, so I will be equivalently happy to read it when it lands on the arXiv, as you prefer :smile:

Hart Montgomery (Sep 15 2021 at 18:13):

Sounds great! I'll ping you when we post a copy on eprint or arXiv. Thanks again for your comments!

Daniele Palombi (Sep 17 2021 at 13:22):

Actually we have a draft where we do quite a bit more, like modeling different "generalised ways of composing" (both in sequence and in parallel, having the latter kind of upgrades our method from FSMs to Petri nets) boolean circuits, doing all this stuff for arbitrary categories and not only for FSMs, etc...

Hugo Jenkins (Sep 19 2021 at 05:52):

Hello! I'm Hugo. I graduated a few months ago from Berkeley, and I hope to apply to a math PhD program this fall.

I would really like to learn more about CT and computation, the fact of a connection between which is awesome. In particular, just from naively reading nLab I'd be very curious to work through a precise description of the Curry-Howard-Lambek correspondence. I've also gotten the idea that categories with various levels of axiomatized structure "admit various computations" like taking pullbacks, factoring morphisms...! And they have different "internal logics", which I don't understand. I'd really like to have an oversimplified model of the circle of ideas here.
I've also just found Lawvere's 1969 article ( http://emis.matem.unam.mx/journals/TAC/reprints/articles/15/tr15.pdf ) seeming to abstract the fixed point approach to the halting problem and Gödel's first theorem (and other stuff) to a property of CCC's. This is all absolutely incredible to me and a lot to take in. Is there any "categorical" model of computation which is Turing complete/nicely related to the classical ones?

I guess the question I'm ultimately going to end up asking here is, what should I do next if I want to seriously pursue these topics? In particular where should I apply to grad school? Many of the non-US centers of research seem to expect a masters before entering their PhD programs.

Anyone's advice, thoughts or reading recommendations would be extremely appreciated. My sincerest thanks to this community for existing and being open; that's another thing I'm struggling to wrap my head around.

Leopold Schlicht (Sep 19 2021 at 11:43):

Hi! This paper by Carsen Berger contains a precise description of the Curry--Howard--Lambek correspondence. (I personally believe the formal Curry--Howard correspondence is somewhat tautological, but it's nice that it's written down somewhere.)

Hart Montgomery (Sep 20 2021 at 17:28):

Thanks for the response! Are you referring to the zk-SNARK paper or your Petri nets paper? Sorry for the confusion! I didn't see you as an author on the SNARK paper.

Daniele Palombi (Sep 21 2021 at 15:53):

I'm refrerring to an unpublished draft I've written together with @Fabrizio Genovese which expands on the zk-SNARKs paper. We should upload it on arxiv but we're both too lazy to get it in a polished enough state and in a LaTeX class that doesn't suck.

Fabrizio Genovese (Sep 21 2021 at 18:16):

Hart Montgomery (Sep 21 2021 at 22:39):

Haha, I know how it is. Let me know when you all get around to posting it! And thanks!

Louis de Forcrand (Nov 16 2021 at 17:05):

Hi everyone! Louis, beginning a masters, currently following a course on categorical logic and topos theory trying to keep my head (or at least some hair) out of the water. There is a non-zero probability that when (and if) I figure out what I'm doing with my life it will involve categories.

I've been here for a while but haven't posted anything yet. Thanks to Morgan and Josh for inviting me!

Leopold Schlicht (Nov 18 2021 at 17:38):

Louis de Forcrand (Nov 18 2021 at 17:54):

Olivia Caramello gives a yearly course on subjects related to topos theory at the master's level at the uni of Insubria. (That's beginning graduate level for y'all Americans out there.) I've heard it is rare to find courses on the subject at that level. Of course one has to hang on tight.

We're very few in class and I'm pretty sure she's OK with anybody who wants to pop in and listen! Classes are given online, and if you're interested you should send her an email.

James Possum (Dec 14 2021 at 00:52):

Hello! I'm brand new to this website and still figuring things out. I am a phd student working on philosophy of physics stuff.

Srikanth Pai B (Jan 07 2022 at 08:02):

Hello! My name is Srikanth and I am a Ph.D student from India. I joined as a physics student but I am working with a mathematician now. I picked up most of the maths in the last two years.. My primary interests are quantum field theories. I am presently interested in Dijkgraff Witten theory and its applications to representation theory.

It's great to see so many prolific math expositors at a single place. I wish to learn a lot from this place and try to contribute whenever I can.

Samuel Steakley (Jan 07 2022 at 22:45):

Hello all! I am a data guy at a municipal health department, though my bachelor's was in physics. As I have confronted my office's deficiencies in the modeling and control of the knowledge that underlies our work, my curiosity led me to read about categorical databases. This and some self-study rekindled my passion for mathematics, especially Statebox's dazzling introductory CT cram course, taught by the lovely @Fabrizio Genovese (thanks for the invite!). Roughly my biggest interests are the engineering, and the physics, of information (systems). I am not totally sure where this new phase of math study will take me (I have recently enrolled for part-time, non-degree study with NetMath at UIUC) but so far I have greatly enjoyed the fascinating discussions that take place here.

Drew Allen McNeely (Feb 18 2022 at 01:56):

Hello everyone! I'm a PhD student in aerospace engineering. My research is in stochastic dynamical systems, and I'm trying to create a library to represent control and estimation schemes using Markov categories. I asked @Tobias Fritz for some help, and in our discussions he suggested I check this place out.

There's a lot I want to do with this library, but I'm just starting to expose myself to the work that others have done in monoidal categories. I'm hoping I can utilize some of it!

Tobias Fritz (Feb 18 2022 at 07:05):

Dario Stein (Feb 18 2022 at 21:04):

Hi @Drew Allen McNeely , I'm also interested in Markov categories and conditioning! Have you checked out my little implementation here? Feel free to let me know if you have specific things in mind with your library

Drew Allen McNeely (Feb 23 2022 at 22:09):

@Dario Stein This is super interesting! Do you plan on extending to other Markov categories aside from Gauss? That's what I'm trying to do currently, but I often get stuck.

Benjamin Merlin Bumpus (he/him) (Feb 24 2022 at 10:58):

Hi everyone, I'm a Postdoc in graph theory and computational complexity who's recently started to transition into applied category theory.

I work on structural graph theory (mostly) and I study so called 'recursive graph decompositions' (i.e. tree-width, clique-width etc etc). Lately my work has started to focus on categorical characterizations and generalizations of these graph-theoretic notions.

It's pretty cool that this community exists, so thanks for having me! I look forward to meeting you all :)

Graham Manuell (Feb 24 2022 at 12:08):

Hi @Benjamin Merlin Bumpus. There was recently some discussion about if/how category theory might be applied to graph theory here. I'm sure people would be interested to hear your perspective.

Jules Hedges (Feb 24 2022 at 12:10):

Benjamin Merlin Bumpus (he/him) (Feb 24 2022 at 12:43):

Benjamin Merlin Bumpus (he/him) (Feb 24 2022 at 12:47):

and, @Jules Hedges , thanks for the link; I saw this on Twitter last week and it seems rather interesting!
Kocsis and I also considered a similar topic (although our methods are very different from Paweł and Elena's) by introducing 'Spined Categories' (which you can find here: https://arxiv.org/abs/2104.01841 <--- a new version should hit the arXiv next week)

(b.t.w. it's my first time using Zulip, so apologies if I'm using it wrong.. are there specific ways for replying to messages that are preferred here?
)

Morgan Rogers (he/him) (Feb 24 2022 at 22:06):

No, don't worry, we don't constrain how people chat here for the most part. Welcome!! :big_smile:

Mattia Villani (Feb 28 2022 at 19:17):

Hi all! First time on Zulip :) I'm a PhD student in the CDT for Safe and Trusted @ King's & Imperial College London and I'm working with category theory in geometric deep learning - trying to use CT for explainability techniques and finding safe ways of using AI. Generally trying to find out what neural nets are thinking most of the time :) Exciting to be here with the big names!

Peter Arndt (Mar 02 2022 at 20:07):

Sounds cool! Is there already something to read, or a talk to watch, about category theory in geometric deep learning?

Fawzi Hreiki (Mar 03 2022 at 10:43):

Nice to see another King's student around. I did CS then mathematics there myself.

Jacob Zelko (Mar 04 2022 at 05:22):

Hi everyone!
My name is Jacob Zelko and I am a researcher at Georgia Tech Research Institute and the Centers for Disease Control.
I have formal training in biomedical engineering, biomedical informatics, and medical anthropology and currently serve as the PI in an observational health characterization study.

I was exposed almost by chance to Category Theory through working with @James Fairbanks @Evan Patterson @Sophie Libkind and other members of the AlgebraicJulia ecosystem.
I was greatly smitten by the ideas in CT as I had been thinking for several years about knowledge management and information systems - going so far as to read some old papers pertaining to cybernetics and control theory.
When I stumbled across CT, it just made complete sense and I was sold on the idea as it helped me put in order my thoughts on relating the typically unrelatable.
Currently, my interest in Category Theory lies in determining how to compose research studies in order to create novel research studies - especially in the domain of observational and public health research.

As an aside, I have a vested interest in visualization as I am the co-creator of the Julia Animation and Visualization engine, Javis.jl, and am currently exploring methods of creating a tool to create commonly used visualizations in CT research through my small side project, LuxCat.jl, while interoperating within the AlgebraicJulia ecosystem.
Furthermore, I am the author of a small website called Crash Course Category Theory (C3T for short) that contains my notes as a non-mathematician learning CT.

P.S. For fun, here is an animation of an upcoming feature made by a Javis contributor named John and an example of a diagram representing a simple ACSet defined in Julia!

John Baez (Mar 04 2022 at 07:31):

Hi! I'm working with Evan, Sophie and others on using categories to develop software for more easily modified models of infectious disease!

Jake Gillberg (Mar 04 2022 at 14:41):

Jacob Zelko (Mar 07 2022 at 16:09):

Amazing @John Baez !
Do you happen to have any papers published on that work?
I am aware of Semagrams.jl at the moment. :smile:

Also, @Jake Gillberg - wonderful to see you!
SUPER happy to see our worlds colliding!

John Baez (Mar 07 2022 at 16:56):

(and the links therein). But this is from October 2020, and a lot has happened since then!

Eric Schles (Mar 13 2022 at 16:28):

:wave: I'm Eric. 1st year PhD student @CUNY Graduate Center (in NYC) && Principal Data Scientist @Johns Hopkins. I'm interested in the cross section of category theory and machine learning. Looking forward to learning with all of you!

Miguel A. Santos (Apr 29 2022 at 18:47):

Hi I'm Miguel, or rather MA, for short. My life started high in energy (Math. Physics) and I've been gradually radiating off on my way through Stat Mech, Biology and now working in IT. I never found the right/enough time to learn beyond the basics of CT and I'm hoping being here around reading and possibly asking questions may help me get beyond that 101 level. So thanks for having this running and being welcoming.

John Baez (Apr 29 2022 at 18:54):

Hello! Right now you can watch a bunch of us talking about chemistry and category theory at #practice: chemistry. We're just getting started; we'll be meeting at the end of May to work on this.

There's a lot of other stuff going on here, too. I guess you need to subscribe to streams to see what's going on in those streams.

Miguel A. Santos (Apr 29 2022 at 19:48):

Thanks for the tip, @John Baez . It looks like I'm subscribed to everything, so I'd just have to check them out.

AZ Andersons (Apr 29 2022 at 23:06):

John Baez sent me an invite, and here I am. In my retirement from the military-industrial-intelligence complex, I am looking into understanding the universe as it really is and not as one would like it to be. Discovered The Laws of Form while reviewing Stan Tenen's book "The Alphabet that Changed the World." Discovered Burkhard Heim's Extended Quantum Field Theory, and then his Theory of Everything, and realized that the Laws of Form provided the axioms for Heim's Theory. It has been a wild ride since then. Just came to the understanding that, as George Spencer-Brown wrote, if something is obvious from experience, but very hard to prove, then it is probably very close to an axiom of the real world. Turns out the Jordan Curve Theorem is hard to prove because it is a statement of the definition of a distinction in the Laws of Form. This turns topology on its head, and means that the world is quantized by area.

John Baez (Apr 29 2022 at 23:39):

Lawrence Hueston Harper (Apr 30 2022 at 17:02):

Larry HarperI am Larry (Lawrence Hueston on the list of users) Harper, Professor Emeritus in Mathematics at UC Riverside. I have been applying CT to combinatorics since 1965 when I discovered a notion of morphism for Ford-Fulkerson flows on networks. After several years of proving Sperner-type theorems for ranked posets (the largest antichain is the largest rank) using FLOW morphisms, I decided to look for morphisms of other combinatorial problems. I did not have to look very far: My first paper (1962) had solved the edge-isoperimetric problem on the graph of the n-cube and I realized that the techniques that I and others had used to solve similar problems on combinatorial structures were actually morphismological. The morphisms for those problems were analogs of symmetrization, the transformations that Jakob Steiner had used in 1840 to give the first rigorous proof of the classical isoperimetric problem in the plane. So I called the morphisms for combinatorial isoperimetric problems "Steiner operations". In 2004 I published a monograph on Steiner operations entitled, "Global Methods for Combinatorial Isoperimetric Problems". Currently I am writing another monograph entitled, "The Morphismology of Combinatorics" to summarize what I have learned since1965 about the application of morphisms and the categorial structure they generate to solving combinatorial problems.

Dean Young (Apr 30 2022 at 19:41):

Hi all. I’m Dean. I was glad to join since I was just thinking about the Baez Dolan perspective on entropy. The paper they have axiomatizes entropy but the proof itself recourses to the old view in a sense. I thought folks might like to hear about the proof I found which is both simple and stems purely from the axioms Dolan and Baez came up with (which resemble the axioms of K_0).

John Baez (Apr 30 2022 at 20:10):

It reminds of this story: once I was at a conference and a Japanese fellow came up to me. After shyly standing there for a little while, he said:

John Baez (Apr 30 2022 at 20:11):

Dean Young (May 01 2022 at 01:30):

Dean Young (May 01 2022 at 01:55):

K0(R) is isomorphism classes of objects in Projective R-mod with inverses formally added in.

Dean Young (May 01 2022 at 01:57):

John Baez (May 02 2022 at 20:13):

Jacob Chateau (May 06 2022 at 13:37):

Hi there everyone! I'm Jake! I've been into categories since I feel in love with algebraic topology, and naturally found myself diving deep through the nLabyrinths. I've been influenced by the ideas of too many of the incredible names I see in this chat. I've been hoping to join for a long time, and it's a pleasure to be invited here. Thank you, @Sam Tenka ! I am also a friend of @Dean Young , who I see just joined too.

My main interests are spread all over all the places. Haha... but lately I have been thinking about 'everything classifies something', univalence, holography, modulation, modality (cohesion etc), tangles, cobordisms, groupoidification, species, Goodwillie, Chu and (co)bar stuff, coends, 'tensorality'. Idk, just kind of my palette of ideas, connotations and contexts.

I have a strong desire to see stuff synthesized, and I contemplate my measures of pleasures in these syntheses. I think about variation–integration in analogy to analysis–synthesis, and I wonder if higher (co)monadic, spherical diagrams and their duals can capture nestings of modalities. I use cooking metaphors a lot, like 'this geometry tastes spicy and slightly under-baked'. (Sidenote: do you think we might benefit from topologizing qualia? It might taste good idk/lol)

Sorry to make such a long introduction. Like I said, I am really happy to be here! :peace_sign:️

Oscar Cunningham (May 06 2022 at 13:41):

Todd Trimble (May 06 2022 at 14:05):

I'm actually not sure what "tensorality" is, but it reminds me of Wessonality. :-p

Jacob Chateau (May 06 2022 at 14:11):

Haha, neither am I really. What kinds of shapes of qualities do all 'tensor things' share? That would be my initial qualification of the neologism, beyond it having a slight ring to it. Maybe 'tensorality' is better, or just different. But I do think about co-Yoneda and whatever higher double categories should be, and Loregian's(?) 'Einstein notation for profunctors'. Can we have 'coordinate-free' functor calculi like how we do coordinate-free differential geometries? Idk, but THAT should be 'tensorious' in my book, hahaha

John Baez (May 06 2022 at 17:33):

Todd Trimble (May 06 2022 at 18:48):

Simonas Tutlys (May 07 2022 at 16:52):

As I haven't formally introduced myself,Hello there :) My journey into category theory is/was very chaotic - while in the first year of a CS degree I noticed that every seperate topic had 'structures' and 'things going between them' and also bought an ereader so I basicaly burned myself out of uni (which i was doing better than school at) by going deep into the CT rabbit hole with various branches of math before and after that (information theory for example).one of my favourite subbranches are categorical logic/semantics and internal structures and i've been thinking about how to apply the 'structural' part of category theory to the current wave of machine learning/AI ever since to make it less throw-stuff-at-the wall-and-see-what-sticks.For personal reasons (the burnout being the main one) experimenting with my ideas practically in code is hard for me.Also,sometimes I dip into developing small games or if i get an idea for an interesting mechanic (usually involving some form of procedural generation,one book put it nicely - it feels like you're playing with infinity),but that's just basically developing coalgebras with the players' actions (or lack thereof) as the transitions :) experimenting with ML is hard cause of the compute requirements but I had some small victories there.Basically currently I'm a madman stuck in the nLabyrinth :D

Franklin Pezzuti Dyer (May 07 2022 at 17:10):

Neat - what is the relationship between coalgebras and procedural generation? (although, as a disclaimer, idk anything about coalgebras really )

Simonas Tutlys (May 07 2022 at 17:49):

That was meant to be to seperate things mentioned but since you ask,I have one idea for using discrete AI planning (STRIPS formalism for example) to try to procedurally generate puzzles,quests etc.There's already a paper on this but not exactly what i have in mind - basically doing the reverse of planning - generate the sequence of actions first (the puzzle,which could be constrained in various ways),and then generate the strating situation in which that plan could be executed.And since planning formalisms are basically a complex labelled transition system (guess) thats the connection with coalgebras :) I already have a very buggy procedurally generated puzzle game up.

coalgebras,as I see them,are an abstraction of moving around a statespace constrained by the actions available.

Jacob Chateau (May 08 2022 at 13:01):

This is amazing! I dream of an abstract machine that procedurally generates procedural generators, and to describe it using 'higher adjunctions' in (∞,∞)-categories (better names are out there I am sure). But imagine if we could model, say, Dwarf Fortress, using a basis of nice constructor constructors? The 'Calculus of Constructions' has proven very adaptive, I don't see why we can't dream in that direction.

Simonas Tutlys (May 08 2022 at 14:48):

I haven't yet grasped what the two numbers (n,m)-category mean but am familiar with enriched/n-categories.The intuition for adjunctions that finally stuck with me and i wrote about in the 'around machine learning' thread is an information theoretic one,but why do they give rise to (co)monads/nice (co)algebras is still beyond me.Good to know there are people thinking about PCG and CT though :)

John Baez (May 08 2022 at 17:10):

An (n,m)-category is an n-category where the j-morphisms with j

>

m are invertible (or more precisely, equivalences). For example a groupoid is a (1,0)-category.

John Baez (May 08 2022 at 17:11):

Thus,

(\infty,\infty)

-category is a complicated way to say

\infty

-category.

John Baez (May 08 2022 at 17:14):

There's been a lot of work on

(\infty,1)

-categories, and a certain amount of confusion due to the fact that Lurie decided to call these

\infty

-categories, presumably to make his book on the subject 10% shorter. (It's now only 735 pages long.)

Simonas Tutlys (May 09 2022 at 04:07):

Davi Sales Barreira (May 13 2022 at 16:15):

Hello everyone. My name is Davi, I'm a PhD student in Brazil at EMAp - FGV. My thesis is in Category Theory applied to data visualization.

Carlos Zapata-Carratala (May 24 2022 at 21:08):

My name is Carlos Zapata-Carratala. I finished my PhD in the School of Mathematics of the University of Edinburgh a couple of years ago and I am currently the president of the Society for Multidisciplinary and Fundamental Research while I continue with my mathematical research and look for postdoc positions. I am currently based between Edinburgh (UK) and Alicante (Spain).

I first came across category theory due to my work in differential geometry and the mathematical foundations of physics. I was introduced to the subject by Tom Leinster and his students here in Edinburgh. I have recently refocused my interest in category theory due to my current research on higher order systems and, in particular, higher arity structures in mathematics, physics and computer science.

The main goals of the higher arity research project (which I lead) are outlined in our website that went online recently:

Athough the project as a whole is highly interdisciplinary in scope (we have collaborators ranging from biology to art history), what pertains to category theory, and the reason I am excited to join this online community, is that we are looking for higher arity generalizations of the basic notion of category. This means, in particular, increasing the number of objects related by morphisms in a way that is generally non-sequential and doesn't necessarily conform to an input-output framework. Notions such as operads and poly/multicategories (and their higher generalizations) are steps in the right direction for the sort of generalizations that we are searching for, but they are still firmly anchored in sequentiality and input-output, i.e. they are all largely formulable in terms of directed graphs, put simply "they are mostly about arrows". The idea is to take (directed or otherwise) hypergraphs as a starting point for higher arity analogues of category-like objects.

There is some work on this topic of higher arity categories from Topentcharov in the 1980s but it doesn't seem that much more has been done in that direction. Any pointers to relevant literature are greatly appreciated. We have rediscovered an example of a known structure called a heapoid (a partial ternary operation satisfying a slight modification of associativity) where our approach seems to clarify things greatly and it paves the way to finding meaningful n-ary generalizations of associativity. We describe this in our recent paper:

Sam Staton (May 24 2022 at 21:25):

Hello @Carlos Zapata-Carratala! This sounds curious. I have been interested in things like star poly-categories which can be described without talking about sources and targets -- just a set of objects and for each sequence of objects a set of "morphisms", respected by permuting the sequences (see nlab link). There are category-like examples, but also less category-like examples such as

[0,1]

. Does this fit into your formalism? Apologies if I misunderstood.

Nathanael Arkor (May 24 2022 at 22:14):

You may also be interested to look into operadic categories, which are a generalisation of structures that be described by "pasting schemes".

Carlos Zapata-Carratala (May 24 2022 at 22:36):

That does follow the general ideas that we are interested in, as I mentioned polycategories are instances of higher arity generalizations of categories. The problem that I see with polycategories is that they are not very "primitive" as n-ary structures in the sense that composition is still a binary operation on morphisms. An easy example of a ternary (pre?)category is the class of sets and ternay relations. If we understand composition as a generalization from binary relations, i.e. an operation that takes several relations of a fixed arity and gives another relation of the same arity (the usual case is a pair of binary relations compose to give another binary relation, which in our eyes is the prime example that motivates the usual definition of composition of morphisms in categories), then there are many posibilities. In section 4.3 of our previous paper we identify at least 10 different well-defined composition operations taking trios of ternary relations on sets: https://arxiv.org/abs/2201.09738. This means that if there exists a satisfactory definition of "ternary category" understood as a collection of objects and ternary morphisms that compose in a particular way, it is far from being unique.

Jacques Carette (May 24 2022 at 22:39):

Is there an ELI5 introduction to operadic categories and "pasting schemes"? As an example of what I'm looking for: both the original Joyal paper and the Bergeron et al book on Species is a comfortable read for me. Something like that.

Jules Hedges (May 26 2022 at 10:57):

Hi! :wave: There's a bunch of people in Glasgow who might be interested in talking, want to come and visit us some time?

Carlos Zapata-Carratala (May 27 2022 at 11:00):

Mohamed rashad (Jun 13 2022 at 22:45):

Hello all,
I'm Mohamed Rashad, MSc. Student in Computer Engineering at AAST Cairo, Egypt.
I do category theory for Machine learning mainly for my degree, and I've been studying Applied CT for the past 2 years,

I actually "discovered" category theory in my undergraduate years, when I was studying electronics/comm related topics and software at the same time, and I found by intuition that we can move between electronic/control/signal/comm systems almost easily using some informal ways (you know, engineering hacks and so), and it's accepted in the industry, while also having good models for these systems (I can easily verify the correctness of any electronic circuit for example).. yet I didn't find this in the software world, where everything seemed to be like plumbing to me, and only making things work-ish.. so I started researching how to use control theory in designinig software, while studying abstract algebra on the side.. one thing and the other, I was studying theoretical CS and going through Curry-Howard-Lambek correspondance, that's when I discovered category (and type) theory.. and I explored some articles and stuff.. then it all linked together and It's like I've found my lost child :D

Since then I've been dedicating myself to category theory (and with less attention type theory).. in order to explore this area, and help bring these amazing tools of categorical thinking to the industry.. which is influencing my MSc. work right now.

Anyway, long intro, I'm very happy to be around, also thanks to @Jules Hedges for the invitation :victory: hope I can be an addition to the community :smiling_face:

Karem (Jun 14 2022 at 02:09):

I am Karem, PhD student from University of Alberta. I never introduced myself here. So here it is!

I am algebraic geometry PhD student currently working on regulator problems from Higher Chow groups and different variants of such. I proved surjectivity for different variant of higher Chow groups that my supervisor invented. Apparently also these variant could be used for Physics. I am also very interested in Physics as well so in my spare time I study it. Nice to meet everyone! Hopefully we can have great discussion in future.

Andrii Berezovskyi (Jun 14 2022 at 14:12):

I am Andrew, a PhD student at KTH Royal Institute of Technology. I work with semantic web technologies and their application to the cyber-physical domain to make communication between machines more intelligent. I got interested in CT (through the wonderful "7 Sketches" book) as the means to capture the semantics of the CPS deeper than semantic web technologies allow today.

Right now I am learning bisimulation and coinduction by going through (Sangiorgi 2011) on my own in order to study the properties of federated rule execution, but feel that I need some help. I colleague of mine suggested to sign up in this group to search for a tutor. Is there a specific stream where one could post messages in search of a private tutor?

John Baez (Jun 14 2022 at 14:19):

I haven't seen requests for a tutor here, but if you're offering to pay someone to be a tutor, I guess

Tom Hirschowitz (Jun 15 2022 at 08:22):

To add to John's message: some of us are indeed familiar with bisimulation and coinduction. But there is a lot of non CT-related material in this book, and I'm not sure whether such questions would be welcome here. Maybe the @moderators could tell us?

Matteo Capucci (he/him) (Jun 15 2022 at 09:21):

I take a 'lazy' approach to police in/off-topicness. I'm sure Andrii will be reasonable. If a question attracts attention then it's fine for me. Also #general: mathematics can work for something a bit less categorical than usual.

Guillaume GEOFFROY (Jun 15 2022 at 14:57):

My name is Guillaume (french for William). I am a M2 student at Université Paris-Cité. Actually, it is my second one. The first one was about theoretical physics (gauge theories and differential geometry).

My interest for Physics lead me to the duality between algebra and geometry. A big part of it is Isbell duality. To take into account any kind of algebra, I have learnt enriched category theory. Until today, I have studied algebraic geometry, a bit of differential geometry and of homotopy theory. I am also interested in what logic can tell us about algebraic and geometric structures, also I have some basis in mathematical logic, but less than any mathematical logic M2 student.

To sum up, nowadays, I am interested in all the applications of enriched category theory (especially Physics and Logic) and all what can give a new viewpoint on this.

Matthew Beaudouin-Lafon (Aug 16 2022 at 22:09):

My name is Matt Beaudouin-Lafon, I'm a PhD student at UC San Diego working on Human Computer Interaction. I'm interested in developing methods to help designers make more powerful and more consistent user interfaces. That has led me to trying to clarify what it means to design user interfaces, which has led me to Category Theory (via 7 Sketches). Right now I'm learning about databases and state machines, but I get easily distracted :smile:

Beppe Metere (Sep 09 2022 at 12:14):

Logan Hyslop (Sep 10 2022 at 23:01):

Hi everyone,
I don't think I've introduced myself yet (possibly because I didn't realize there was an introduction channel, but shhh...).
My name is Logan Hyslop, I am an undergraduate at UCLA, currently entering into my second year. I'm currently just exploring my interests, but I quite enjoyed reading condensed math and now analytic geometry, I like categorifications so I am very excited that Professor Rouquier is teaching a course on higher representation theory this Fall, especially since I took a course on Khovanov homology last Spring which was quite fun. I am currently also working on learning infinity category theory, through Riehl's text, which I really really really enjoy reading (it's an amazing book so far and I will talk about it constantly with whoever will listen).
Some other things about me, pronouns he/him/his, I have ADHD, and enjoy sailing. I actually set up a webpage recently (though it definitely needs a lot of work before it's actually any decent).
I guess that's my introduction, so :wave:.

Jason Parker (Sep 12 2022 at 17:35):

Hi everyone,
I just joined the category theory zulip last week! My name is Jason Parker, and I'm currently starting my third (and final) year as a postdoctoral researcher at Brandon University in Brandon, Manitoba, Canada, working with Rory Lucyshyn-Wright. I'm especially interested in enriched algebraic theories and monads and their various applications to mathematics and computer science, and I've recently developed an interest in applied category theory as well (especially applications of category theory to databases). My website is https://www.jasonparkermath.com/. Before starting this postdoc, I did my PhD at the University of Ottawa on isotropy, a topic that was co-invented by one of my advisors, Pieter Hofstra, who died unexpectedly this past spring. Philip Scott was my PhD advisor as well. I will write a more detailed post in the "our work" stream sometime this week!

Matthew Snodgrass (Sep 14 2022 at 13:20):

Hello, I'm Matthew Snodgrass. I'm a freshman at Carnegie Mellon University. My main interest is algebraic geometry but I'm also interested in learning about logic. I like study groups and working with others, if anyone wants to work on learning some AG or categorical logic.

Michael Stone (Sep 14 2022 at 14:36):

Greetings -- I'm Michael Stone, and I'm a mid-career technology generalist with experience and interest in systems, safety, security, software development, ML, NLP, and an undergraduate math background from a decade ago that included a summer research experience focused directly on 2-categories, string diagrams, and Moggi's paper on monads.

Michael Stone (Sep 14 2022 at 14:38):

(My website is https://mstone.info. Anyway, in recent months, I've spent some quality time thinking about algorithms for drawing diagrams, particularly a flavor that is commonly used for depicting hierarchical control systems in some corners of the systems engineering world, resulting in a free software package, https://mstone.info/depict/ + https://github.com/mstone/depict, which I have recently become re-interested in categorifying / formalizing.)

Michael Stone (Sep 14 2022 at 14:41):

(Specifically, one aspect of this software that I am interested in studying more carefully is an observation that the drawing process I have discovered, bugs notwithstanding, seems to me to be expressible as a composition of a series of ~4 information-preserving transformations or elaborations that each have the flavor to me of being possible compositions of adjoint functors -- although I am unfortunately still at the very beginning of trying to formally state and then check this intuition.)

Hugo Bacard (Sep 14 2022 at 20:56):

I’m Hugo Bacard. I’ve been hanging around for while but I'm kind of a "e-shy" person. I think it's time to introduce myself :). So far my interests were in homotopy theory, especially in [weakly] enriched category theory. I would like to learn and do a research work in applied category theory and in ML. I live in the Paris area (in France :D).

Amartya (Sep 16 2022 at 13:44):

Hello everyone,
I learned about CT Zulip thanks to Prof Dmitri Pavlov, who was kind enough to send me a link.
I've been here for some time now but have never introduced myself yet (maybe because I'd never given that a thought until now). So here it comes.

I'm Amartya, an undergraduate student interested in (stable) homotopy theory, higher(model) category theory, higher topos theory, HoTT and categorical logic. I've also recently been interested in Higher Algebra, Higher Operadic stuff and intermediate model structures on simplicial presheaves. I've also been thinking about higher realizability models of HoTT for some time now, which is a work in progress(about which I'll talk a bit at CaCS 2022). Some more details may be found on my website, which I set up recently (which needs a lot of work, to be fair).

Siavash Sakhavi (Oct 06 2022 at 14:45):

Hi
I'm Siavash from Singapore. I'm very interested in the topic and I can't wait to learn more!

Jacob Chateau (Oct 08 2022 at 11:32):

Hi! My persona and identity experience perpetual fluctuation, much like your own. I feel little conflict in re-presenting my self here once more.

My name is Jacob, from Detroit. I care deeply about life and consciousness, and I design schemata for embodied cognitive autopoesis and other funny tricks of the virtual body.

I help design AGI and synthetic lifeforms through an alchemical process we call xenomorphosis.

My species is not yours, but our species are one another's! Let's enjoy a brighter day than yesterday could have ever been.

Morgan Rogers (he/him) (Oct 08 2022 at 18:23):

Ryan Wisnesky (Oct 11 2022 at 22:21):

Hi All, with the permission of the original authors I'd like to announce a new book on applied category theory. "A Categorical Defense of Our Future: is the first book about category theory written for business leaders and business owners, CEOs, and executives.
Anyone who deals with large-scale challenges around data, safety, and systems will find this book to be required reading.
The authors Brandon Baylor and Esteban Montero are MIT-educated senior engineers. Between them, they have four master's degrees and nearly thirty years of engineering experience at global companies." https://www.yahoo.com/now/time-radically-approach-challenges-modern-121400881.html

Henry Story (Oct 11 2022 at 22:24):

Lucia (Oct 16 2022 at 20:16):

hello, I am Lucia and I am very interested in the applications of CT for Game Theory. nice to meet you all!

Matteo Capucci (he/him) (Oct 17 2022 at 15:59):

Lucia (Oct 17 2022 at 17:21):

Yes, we can chat or discuss at any time. I do cooperative games, mostly. and of course, stochastic games.

Jeremy Sawruk (Oct 17 2022 at 20:38):

Hi, I'm a software developer at a very large tech company working on responsible and interpretable AI

Matteo Capucci (he/him) (Oct 18 2022 at 19:21):

I've mostly worked in non-cooperative games bc I didn't figure out yet a good way to handle cooperation, but I'm very interested in the topic. Let's chat soon!

Doug Needham (Oct 28 2022 at 12:44):

Hello. I am Doug Needham. I am an amateur mathematician, but a professional Data Person. So I do get to work with a decent amount of data, and a few algorithms. This class has been great. Nice to meet everyone.

Morgan Rogers (he/him) (Oct 28 2022 at 16:42):

Doug Needham (Oct 28 2022 at 17:37):

Marco Lin (Nov 03 2022 at 08:46):

Hi I enthusiastically follow some CT people on twitter and got an invite ages ago. I got excited seeing TDB's post on the Entropy chain rule and topology * algebra, and possible connections with Jules Hedges' and Matteo Capucci's work. And now I'm very interested in what the status is on CT inspired AI/ML innovation! I don't understand the deep maths though, my background is in neuro and psychology :see_no_evil: But conceptually, I find it all very fascinating. Great to see you all!

Alonso Perez-Lona (Nov 15 2022 at 04:00):

Hi everyone. My name is Alonso Perez-Lona, and I'm a Physics grad student mainly interested in the emergence of homotopy theoretical structures in String Theory. I've been looking for an active community focused on these topics, and Professor Pavlov kindly shared this link with me. I am also interested in Top and CT on their own, as well as in Philosophy, Religion, and Psychology to some extent. Always delighted to converse on these or else.

Jean-Baptiste Vienney (Nov 15 2022 at 10:51):

Alonso Perez-Lona (Nov 15 2022 at 16:11):

Jean-Baptiste Vienney (Nov 15 2022 at 17:21):

Alonso Perez-Lona (Nov 15 2022 at 19:57):

I did my undergrad there, graduated last year. I mostly worked with Hisham Sati and sometimes with Urs

Javier Calvo-Amodio (Jan 04 2023 at 22:50):

Hi everyone, I'm Javier Calvo, an industrial engineering faculty at Oregon State University (I met some of you at the NIST workshop last November). My main research focus is on systems science and how it relates to systems engineering and the purposeful human activity systems that make it work. I am in no way well versed in CT, but I believe that since CT and systems science are both transdisciplinary in nature, there is a path to integrate both to formalize systems science and to enhance the perspectives CT possesses (I admit this possibility may already exist within CT, but with your help and guidance we can make the relations explicit).

Spencer Breiner (Jan 05 2023 at 01:32):

Javier Calvo-Amodio (Jan 05 2023 at 01:43):

Aaron David Fairbanks (Jan 08 2023 at 20:02):

I finished a master's degree in math at Edinburgh a year and a half ago, with a dissertation on topology and category theory. (But I'm originally from Boston.)

I'm a big fan of the contributors to the n-Category Cafe. And I've learned a lot through the nLab. I like multicategories and PROs and PROPs and other gadgets like these. I'm particularly interested in coming up with simple visual ways to think about things.

I'm currently finishing up PhD applications. If anyone has any pointers for places/people to apply to, with deadlines that still haven't expired, I'd appreciate them.

Benjamin Lyons (Feb 03 2023 at 01:28):

Hi everyone, I'm Benjamin Lyons. I did a BS in economics at George Mason University and am now studying abstract maths as a non-degree student at the University of Colorado Denver. I'm hoping to study category theory in graduate school, with an eye toward applications in economics and neuroscience. If anyone has any ideas about places or people to reach out to in pursuit of that goal, I'd greatly appreciate it. Also, if you want to talk about category theory and what it might mean for econ/neuropsych, let me know.

John Baez (Feb 03 2023 at 01:36):

Did you consider getting a PhD in, say, neuroscience and trying to also work with some category theorists? If you get a PhD in neuroscience you're more likely to get a job, I suspect.

John Baez (Feb 03 2023 at 01:38):

The only person who comes to mind when I think "neuroscience and category theory" is Kathryn Hess. In the very first applied category theory conference she gave this talk:

John Baez (Feb 03 2023 at 01:38):

John Baez (Feb 03 2023 at 01:39):

John Baez (Feb 03 2023 at 01:42):

Benjamin Lyons (Feb 03 2023 at 01:45):

Getting a PhD in neuroscience is an interesting suggestion. My concern would be that I'd be much more interested in learning and exploring math than running test participants in lab experiments. But my brother is a neuroscience graduate student, so I will ask if he thinks there's a way for me to fit in. On the whole, I prefer abstraction, but it's definitely work exploring.

Thank you for the recommendations! I'll ask my brother about Kathryn Hess and reach out to Jules Hedges.

John Baez (Feb 03 2023 at 01:53):

If your main desire right now is to learn lots of math then a math PhD is the way to do that. Working on neuroscience with Kathryn Hess would probably be interesting if you can manage it, since she's a mathematician with lots of neuroscience collaborators, so you might get a math PhD but do work connected to neuroscience. But a European graduate program is very different than a US one: my impression is that you have to hit the ground running, not spend your first two years taking courses like grad students do in the US.

Benjamin Lyons (Feb 03 2023 at 01:56):

Moving to Switzerland would certainly be interesting. I'll be sure to explore these options. Thank you very much!

John Baez (Feb 03 2023 at 05:32):

Jules Hedges (Feb 03 2023 at 10:04):

Jules Hedges (Feb 03 2023 at 10:05):

Econ is a big subject... I can tell you something about category theory + micro, right now I don't think anyone's actively working on category theory + macro

Jules Hedges (Feb 03 2023 at 10:08):

For neuroscience there's also @Toby Smithe (who's nominally here but I think rarely logs in), he recently dropped his PhD thesis about category theory and very theoretical neuroscience, free energy things

Benjamin Lyons (Feb 03 2023 at 19:16):

Thanks! I've seen Toby Smithe's thesis, it's very impressive. As far as economics goes, I'm specifically interested in using category theory to better understand the subject of externality, which would fall into microeconomics. Have you ever thought about applying category theory to externality?

Patrick Nicodemus (Feb 04 2023 at 02:46):

Patrick Nicodemus (Feb 04 2023 at 02:47):

Patrick Nicodemus (Feb 04 2023 at 02:49):

Benjamin Lyons (Feb 04 2023 at 04:00):

Brendan Murphy (Feb 15 2023 at 22:47):

Hi everyone! I'm a math PhD student at the University of Utah interested in category theory (especially in applying homotopical and higher categorical methods in commutative algebra and algebraic geometry)

Patrick Nicodemus (Feb 15 2023 at 23:43):

Adam Nemecek (Mar 02 2023 at 20:45):

Hey gang, excited to be here. I'm a programmer with a decent knowledge of math, physics and such. I have recently published a paper where I argue that Hopf algebras can be used as a foundation of convnets, transformer models and diffusion models https://arxiv.org/abs/2302.01834. I just finished a convo with @Andrew Dudzik who has been arriving at some of the same conclusions from a different angle. I expect a lot more CT in machine learning in the nearby future.

Jean-Baptiste Vienney (Mar 02 2023 at 21:08):

I don't understand what is the coproduct of a combinatorial Hopf algebra? You say that it is the shuffle product but it is a product and not a coproduct, no?

Adam Nemecek (Mar 02 2023 at 21:38):

Benjamin Grant (Apr 04 2023 at 18:51):

Hi folks! My name is Ben, I’m a current senior math (& environmental studies) major at St. Olaf College. At the moment, I’m waiting to hear back from a few PhD programs in math I’m waitlisted at, hoping to get some good news soon.

I’ve been interested in category theory for a little while now, and have been actively digging into it to try to learn more for the past year. I found myself in a weird spot as a math & ES major interested specifically in abstract algebra/topology— I had no idea how I was going to bridge the gap in my interests and apply abstract math to environmental issues. I ended up stumbling into categorical systems theory about a year ago, though, and that changed a whole lot!

Since then, I’ve been trying to absorb as much category theory as I can outside my coursework. My interests have shifted a little bit away from applied category theory toward higher categories/categorical logic as of recently, but I still love thinking about compositional systems & games!

At the moment, I’m working on-and-off on a hobby project to “internalize Minesweeper and related puzzles” in the language of category theory, and use fixed points/coalgebras of certain endofunctors to study the various levels of “solvability” that a Minesweeper board (or other puzzle, like a Sudoku board or a jigsaw puzzle) can have. I’m pretty close to something really neat, I think, but I also need time to flesh out how exactly I want to organize all the work I’ve done and communicate it to others.

The past couple days, I’ve also been messing around with the idea of using nonstandard-shaped globe categories to define nonstandard higher categories. More specifically, instead of just using finite ordinals/omega to shape a globe category, maybe we could also use larger ordinals or non-totally-ordered well-partial-orders. I would like to figure out exactly which well-partial-orders P admit reasonably-shaped globe categories (if it isn’t just all of them), then take models of those globe categories in Set to make P-graphs. Then, I’d like to construct a monad on the category of those P-graphs that gives the free weak P-category’s underlying P-graph on any given P-graph, and finally look at its algebras. Long term goal is to get to the functoriality of this construction over the category of well-partial-orders and monotone maps between them, and take some sort of Grothendieck construction to be able to talk about functors between differently-shaped P-categories.

That was a lot— got carried away! Wrapping up, I’m happy to be here and I’m looking forward to sharing thoughts & learning more from everyone. Take care!

Light Ediand (Apr 04 2023 at 19:31):

Hi I'm Light currently an undergrad mostly into number theory and just started learning about categories in algebra!:D

John Baez (Apr 04 2023 at 20:57):

Hi! I'm a category theorist trying to learn some number theory. I talk about it with a friend here.

Evan Washington (Apr 04 2023 at 22:50):

Realized I never introduced myself. Hi! I’m Evan, a current PhD student in the philosophy department at UC Berkeley. Before that, I majored in math at Princeton. I consider myself equal parts logician, philosopher, and mathematician. I’m interested in applying formal tools like logic and category theory to enrich and better inform the models and reasoning invoked in philosophy in general and in particular in philosophy of language, epistemology, and philosophy of science.

One interesting project I was involved in as an undergrad can be seen in my thesis advisor’s book, The Logic in Philosophy of Science by Hans Halvorson. My contribution was a proof that a syntactic version of Morita equivalence for first-order theories corresponded to a kind of intertranslatability (see Chapter 7!)

John Baez (Apr 04 2023 at 23:39):

Cool! I think I forgot you were at Berkeley, @Evan Washington. Do you ever make it over to the Topos Institute? It's a short walk.

John Baez (Apr 04 2023 at 23:39):

I'm going there on Friday - but I'll probably be insanely busy. Sometime later I hope to spend a month or two there; it would be fun to say hi then.

Evan Washington (Apr 05 2023 at 17:12):

I haven't had a chance to make it over yet, but some time soon I will! It would be nice to chat with some like-minded people

Kyle Wilkinson (Apr 25 2023 at 13:42):

Hello! I've been lurking for a while, but figured I'd officially join. I am a PhD student in Operations Research, which is an almost entirely applied field. My interest in category theory began informally years ago as a philosophical topic related to complex systems, but only became an earnest effort at formal understanding about a year ago. I exist in a category theory vacuum here, so it's largely a solo effort, and often feels overwhelming. I'd say my level of understanding is medium: I know the basics and have delved into the monoidal category/string diagram world pretty heavily. My formal math background includes exposure to real and complex analysis, linear algebra, abstract algebra, graph theory.

I'm specifically interested in applications of category theory to general optimization duality theory (I've at least reviewed the works of Willerton and Fujii), applications to dealing with large optimization problems, and perhaps as a way of augmenting known relations between group theory and integer programming. In short, I'm really trying to think of ways to truly apply CT in my domain, sort out my half-baked ideas, and press forward.

Steve Huntsman (Apr 25 2023 at 14:21):

@Kyle Wilkinson I've used the notion of magnitude that arises in enriched CT for several optimization algorithms, all on arXiv. TL; DR- the magnitude counts "effective sizes" of points, and "bigger" points are outliers. This can drive an exploration mechanism. There are obvious applications to Bayesian optimization and MCMC that I haven't pursued yet FWIW. Not duality theory but maybe still of interest.

Kyle Wilkinson (Apr 25 2023 at 17:51):

Thanks for the link! My focus is on deterministic optimization, but I will check out the magnitude idea.

Jencel Panic (Apr 26 2023 at 13:31):

I have a computer science / programming background and this is how I discovered category theory.

Johan Felipe García Vargas (Apr 26 2023 at 21:50):

I'm a mathematician from Colombia. My Phd was about Hopf monads and Galois theory. I gave a short talk at EBTC if anyone is interested.

I'm preparing a mini-course introducing Applied Category Theory (mostly based on Seven Sketches) and would appreciate any suggestions.

I joined this Zulip long ago, but remained only as an spectator. Thanks to everyone (specially the maintainers and the more active users) for this wonderful place.

John Baez (Apr 27 2023 at 00:40):

Your talk looks very interesting, judging from a few slides I saw on YouTube. Maybe I'll watch the whole thing - even though I don't like watching videos of math talks!

But I'll still ask: do you have something written, that I can read? I'm really interested in Galois theory and curious how it's related to Hopf monads. I know a bit about monadic descent, but not how Hopf monads make their appearance.

Johan Felipe García Vargas (Apr 27 2023 at 17:01):

Wow, I'm so glad that you find it interesting. The short answer is that geometricaly the descent monad (obtained form the pulllback-existencial adjunction) is always a Hopf monad with respect to the cartesian monoidal structure.
In a sense, Hopf monads are the groupoids on monoidal (not even braided) categories, and augmented Hopf monads the groups.

On written there's a pre-print which still needs some love and my thesis. My suggestion is that you would only need to scan the introduction and sections 2.2, 2.5 and 3.1 of the thesis to get the main ideas.

John Baez (Apr 27 2023 at 20:27):

Okay! I'll look at those. If you don't mind I'll start by asking a question. When I hear "descent monad obtained from the pullback-existential adjunction" I imagine that you're studying a bifibration

p: A \to X

(that is, a functor that is both a fibration and an opfibration) obeying the Beck-Chevalley condition, and a morphism

f: x \to x'

, thinking about the monad obtained by the adjoint functors between the fiber over

x

and the fiber over

y

, as in the Bénabou-Roubaud theorem.

I don't understand this stuff extremely well, by the way, but I've been learning about it recently, and I'm wondering if you are saying that the monad I'm talking about is a Hopf monad (under some conditions).

John Baez (Apr 27 2023 at 20:28):

Anyway, I'll look at your stuff and that should help me understand what's really going on, but maybe you could help me by pointing out ways in which my question is on the right track, and/or on the wrong track.

Johan Felipe García Vargas (Apr 27 2023 at 20:51):

I'm saying something way simpler which (hopefully) imply what you said: if you take a morphism

f: X \to Y

in a category with pullbacks

C

, the pulback functor on the slice categories

f^{*} : C/Y \to C/X

has as left adjoint the existential (just composing with

f

)

\Sigma_f: C/X \to C/Y

; then the monad

f^{*} \Sigma_f

over the monoidal category

(C/X, \times_X, X)

is a Hopf monad.

Johan Felipe García Vargas (Apr 27 2023 at 21:01):

I'm not completely sure, but I think that this theorem asserts that descent data for an

f

in your context corresponds with EM algebras (I like to call them actions) of the monad

f^{*}\Sigma_f

John Baez (Apr 27 2023 at 21:34):

Right; I was mainly using the article to point out various ideas and conditions that tend to show up when we build monads from fibrations, like the Beck-Chevalley condition. But it sounds like you don't use that fancier stuff.

John Baez (Apr 27 2023 at 21:35):

In particular I had thought a 'Hopf monad' was a monad and comonad that fit together in a way similar to how a 'Hopf algebra' is an algebra and coalgebra where the algebra operations are coalgebra morphisms and there's an antipode.

John Baez (Apr 27 2023 at 21:36):

But I already noticed this was probably wrong - and now it's even clearer: for you a 'Hopf monad' is a monad on a monoidal category where the monad structure gets along with the monoidal structure in some way.

John Baez (Apr 27 2023 at 21:56):

Johan Felipe García Vargas (Apr 27 2023 at 22:41):

John Baez (Apr 27 2023 at 22:50):

Johan Felipe García Vargas (Apr 27 2023 at 23:00):

The idea behind Hopf monad definition is that the algebra structure is with respect to functor composition, therefore it's a monad; and the co-algebra structure is with respect to the monoidal product, therefore its a (lax) opmonoidal functor. The compatibility of both structures means that the multiplication and unit are opmonoidal natural transformations. The only dificult ingredient was finding that the antipode is a property and not a structure, a property captured by the invertibility of the fusion.

John Baez (Apr 27 2023 at 23:05):

Nice! I'd like to read the section of your thesis where you use this to prove things about the Galois theory of fields. (I'm trying to learn more algebraic geometry and number theory.)

Frank Tsai (May 17 2023 at 15:06):

I'm Frank. I'm a CS student at SUNY at Buffalo.
I was introduced to category theory last year and started studying it seriously under the mentorship of Ivan Di Liberti.
I'm seeking opportunities to be more involved in this field.

John Baez (May 17 2023 at 15:26):

B. Wilson (Jun 09 2023 at 15:55):

Hello, I'm a Ph.D. dropout, working in the industrial ranks, but a lot of my free time is spent going down nLab rabbit holes. My graduate research was focused on analogues of "smoothness" in discrete manifolds. Currently, I am working through MacLane as well as trying to figure out the intuition behind the delooping of an object.

That said, what pushed me over to actually joining this server is a particular question! I'm reading Baez's 2011 "Division Algebras and Quantum Theory", but the nLab page on Hilbert Space links to an MO post which appears to demonstrate that Hilbert spaces can only ever be real or complex: https://math.stackexchange.com/questions/3625943/can-hilbert-spaces-be-defined-over-fields-other-than-mathbb-r-and-mathbb-c/4184099#4184099. So, I'm wondering what I'm missing. The Baez paper describes K-Hilbert spaces over some normed division algebra K, but the positive definiteness of the inner product uses some mysterious order structure on K that I can't quite figure out. The MO post seems to more carefully worry about this order, but then the conclusion seems to be that quaternionic Hilbert spaces don't exist! What's going on here?

Anyway, apart from the above naïve question, my more general hope is that this chat will seduce me into interesting situations with lots of neat people and beautiful math.

Nathanael Arkor (Jun 10 2023 at 07:19):

finegeometer (Jun 19 2023 at 18:47):

I'm currently an undergraduate in college, and I'm interested in type theory and related areas.

I haven't a clue how to use any form of social media, so I'm a bit nervous about signing up to this Zulip server. But I'm tired of not having anyone to talk to.

John Baez (Jun 19 2023 at 18:52):

Hi! Don't be nervous - we're a friendly bunch here. People are happy to explain things if you have questions, though as usual experts who don't know what you don't know may say a bunch of stuff that's hard to understand.

John Baez (Jun 19 2023 at 18:53):

One thing to know is that there are lots of different "streams", many of which you might not notice unless you look.

John Baez (Jun 19 2023 at 18:54):

I think you can see them if you go here. This lets you see all the streams and also see which ones you're subscribed to. (Please don't create a new stream without talking about it to us first.)

Morgan Rogers (he/him) (Jun 20 2023 at 08:11):

But do create new topics within streams! If you have a question and you don't know which stream to put it in, go straight to #learning: questions , which is one of our most active. If you want to discuss something that isn't (or is only tangentially) category-theoretic, try #general: mathematics. Finally, beware that posts on this server are archived, and that the archives of streams with the globe symbol are also visible to non-members of the forum.

Andrius Kulikauskas (Jun 28 2023 at 03:04):

I am Andrius Kulikauskas. I host Math 4 Wisdom, http://www.math4wisdom.com, an investigatory community for absolute truth. I have a PhD in Math from UCSD in 1993. Category theory is relevant for me as a source of examples, especially the Yoneda Lemma and adjoint strings, where mathematicians seem to apply the cognitive frameworks that I have noticed in the works of all manner of thinkers.

Kirby Urner (Jul 01 2023 at 22:09):

I'm attracted to the vocabulary & concepts of CT in part of by my interest in:
(a) the others it attracts e.g. I know @Andrius Kulikauskas PhD through Math 4 Wisdom (M4W), one of my guides and
(b) my focus on "hypertoons" which feature morphing (shape-changing) scenarios interconnecting key frames or segues, leading to random movies in a hybrid geometric + real world space. I come from a background in philosophy of mathematics.
(c) my focus on "quadrays", a vector space defined by four basis vectors (1,0,0,0) (0,1,0,0) (0,0,1,0) (0,0,0,1), the four corners of a regular tetrahedron, from the center-origin (0,0,0,0) -- how to formally map that to ordinary XYZ vector space in CT language, in terms of isomorphisms etc.

Alexander Kurz (Jul 02 2023 at 10:52):

Hi, I have a student who would want to join Zulip Category Theory ... what would he have to do to join?

Ralph Sarkis (Jul 02 2023 at 10:56):

Jonathan Beardsley (Jul 06 2023 at 05:18):

Hi everyone. I was on here years ago and left for a long time. Now I'm back because I need help thinking about profunctors and promonoidal right Kan extensions and I don't know where else to go, haha.

Andrius Kulikauskas (Jul 09 2023 at 13:05):

@Jonathan Beardsley I can't help you with those topics but I am glad you are here.

Posina Venkata Rayudu (Jul 10 2023 at 02:31):

Hi, this is posina aka lost cause, albeit busy compounding epistemology and ontology into which reality is resolved, constructing the space of all mathematical answers to the question 'what is consciousness?', and, most important of all, trying to get Newton to admit that he failed to abstract the zeroth law of change: Unity-respecting Change!

Morgan Rogers (he/him) (Jul 10 2023 at 07:11):

Julius (Jul 16 2023 at 11:13):

Intro:
I am a fresh beginner to category theory but I’d love to learn by discussion alongside just reading. It really helps me learn that way. If anyone wants to answer my extremely beginners-level questions, I would really appreciate that. Thanks very much.

One often is told to read a textbook, but I strongly prefer to have support via discussion, especially when I am new to a topic. I know I can look up these definitions, but I want to be able to ask intuitively and straightforwardly to make sure I really get it. Is there a best sub-channel here in Zulip for me? I’ll post my current understanding of the above two questions in a little bit. Thank you.

Ralph Sarkis (Jul 16 2023 at 12:14):

Welcome Julius, the default stream for asking most questions is #learning: questions (a moderator could move your questions to a new topic there). Small advice, the first two questions in your intro message are not very prone to enlightening discussions here because we do not know what you already know, so we could give many examples or the precise definitions, but these are already in textbooks, nlab, blogposts, etc. Your later questions with some more detail on your current understanding are way better.

Notification Bot (Jul 17 2023 at 10:11):

Morgan Rogers (he/him) (Jul 17 2023 at 10:13):

Christopher Tapo (Jul 27 2023 at 23:31):

Hi everybody! I'm Chris Tapo; I'm finishing my undergraduate degree at ASU and I'm interested in higher category theory, especially weak n-categories, higher tensor categories, combinatorics for monoidal structures, and coherence theorems.

Steve Huntsman (Jul 28 2023 at 14:33):

Matt Cuffaro (he/him) (Aug 08 2023 at 22:04):

Hello all. I was here whenever this zulip inaugurated (2020?) but also left for a long time. I'm back after attending the ACT 2023 conference.

Fiona B (Sep 13 2023 at 23:02):

Hello, I'm Fiona Blackett, and I'm a first year PhD student interested in differential cohomology, higher geometry, and generally homotopy theory in mathematical physics.

John Baez (Sep 14 2023 at 12:01):

Patrick Nicodemus (Sep 15 2023 at 05:04):

ADITTYA CHAUDHURI (Oct 12 2023 at 10:16):

Please note that this is my 2nd introduction in this forum, as my first introduction was as a 2nd year PhD student, which was 3 years back. The following is my current academic situation.

Hi! it's Adittya. I am currently writing my PhD thesis in Higher Gauge theory at IISER-TVM, India.
My thesis introduces a notion of categorified principal 2-bundle that lives in the realm of Lie groupoids. This thesis investigates some geometric relationships between certain standard notions in classical gauge theory and the theory of fibrations/fibered categories by studying connection structures, gauge transformations, and the parallel transport in these principal 2-bundles over Lie groupoids.

Higher geometry, in particular higher differential geometry fascinates me. Recently, I also got interested in Applied Category Theory and would love to see some interaction between them in future.

Also, I am looking for "Post-doctoral positions in related fields", as I will be submitting my PhD thesis in a month. So, please let me know, if any such positions are available.

David Michael Roberts (Oct 12 2023 at 10:45):

@Fiona B @ADITTYA CHAUDHURI welcome to the club of higher geometry! Feel free to ping me in questions on this.

ADITTYA CHAUDHURI (Oct 12 2023 at 11:42):

Fiona B (Oct 12 2023 at 11:45):

Yes, thank you! It's a really exciting area, I'm looking forward to working with it more

John Onstead (Dec 08 2023 at 04:18):

Hi, my name is John Onstead. I am currently a student interested in learning category theory. I was recommended here by Dr. Shulman, whom I had the pleasure of meeting with the other day! My main reason for learning category theory is that I am currently working on a category theory pedagogy project with many unique twists, whose aim it is to introduce category theory to undergraduates (perhaps ambitiously to be able to introduce it to first or second year undergrads!) It will not be for a long time that I can finish due to slow progress (it took months for me to finally sort of understand the basic machinery of category theory, which is essentially still where I am now), but in the meantime I will try to read some of the posts on here and maybe learn something new!

David Egolf (Dec 08 2023 at 04:35):

Welcome, @John Onstead ! The pedagogy project you describe sounds quite interesting! It's a bit different, but sometimes I reflect that the mathematical structures introduced relatively early on in education (for example in high school) are surprisingly complex. For example, a great deal of focus is placed on the real numbers, and the real numbers have a lot of structure! (In the setting of the real numbers we have an ordering, we can add and subtract, multiply and divide, and we can talk about limits of sequences.) By contrast, the concept of a category seems simpler in some ways (at least to me). So sometimes I wonder if it could be helpful to introduce arguably simpler things like monoids and preorders (and maybe even categories) before focusing so much on the real numbers!

Mike Shulman (Dec 08 2023 at 04:50):

John Onstead (Dec 09 2023 at 02:09):

@David Egolf You're very right! Learning category theory has actually given be a much different perspective on mathematical objects than I had before. It allowed me to realize certain mathematical objects are not made of one cohesive structure, but can be represented as continuously building up more and more structure onto something. For instance, the real numbers as you describe, seem like a logical conclusion if you are building up from natural numbers using recursion (IE, from something like the Peano axioms). However, in category theory, that same construction is some underlying set (the set of real numbers) plus the structure of a topological space (the real line) plus the structure of an ordering/poset (where one number is "less than" another number) plus the structure of a field (to add, multiply, subtract, and divide). Euclidean space is another one of these, where one has an underlying set of points (underlying set) PLUS a topology (topological space) PLUS a metric (metric space) PLUS a differentiable structure (smooth manifold) PLUS measures (measureable space) PLUS a way of assigning vectors (vector space) and so on. Decomposing Euclidean spaces in this way really put things into perspective for me of how this seemingly natural structure, where deciding to do various things within it seemed natural and intuitive, was in fact some crazy mathematical convergence of all these concepts.
Also, I've read some of your questions, they're quite similar to ones I have, so I look forward to reading more of them!

David Egolf (Dec 09 2023 at 02:56):

That's a great explanation @John Onstead! It's interesting how certain mathematical structures can feel basic and intuitive, and simultaneously be a "crazy mathematical convergence" of a plethora of concepts.

It's great to hear that you're looking forward to more of my questions! (I don't seem to be running out any time soon, so I'm sure there will be more to come...) But also - if you have similar questions, and you feel inspired to discuss them, please consider posting them on this zulip! I hope you'll find it can be quite fun and educational to do so. In general, I think a variety of questions at a variety of levels is part of what can help keep this community healthy and active.

Adam Millar (Dec 12 2023 at 16:30):

Hello!
My name is Adam and I am a lover of logic, tentatively returning to the world of category theory.

I came to the world of pure mathematics via philosophy. I did my undergrad at Princeton 2011-2015, where I worked with Hans Halvorson, who works on category theory applications to logic and the philosophy of science.
I took courses like Formal Logic, Mathematical Logic, Philosophical Logic, and Set Theory.
I fell in love with the methods and subject matter of mathematical logic.

It was empowering for me to learn that a great deal of mathematics can be understood in terms of formal definitions and which statements entail others. An 'intuition' or ability to 'visualize,' while often useful, was not necessary.
One can construct a rigorous and accurate proof using only an understanding of the logical structure of definitions and theorems. One can engage 'semantically;' What is true? or 'syntactically;' What can I derive?
AND the two perspectives are connected.
This ‘logical’ perspective allowed me to be successful in standard mathematics courses like Real Analysis, Topology, and Graph Theory, beyond the world of logic and foundations.

I was encouraged by Hans to take his course in category theory for undergraduates.
I was further enticed by the promise that recent work in logic used categorical methods, and that category theory was proposed as an alternative foundation by philosophers of mathematics.

It is a bit bizarre because I entered this course (as well as later pure math courses) with really only a logician's perspective; category theory was another formal theory that could be investigated, so I learned 'synthetic' category theory only, before encountering, say, abstract or linear algebra.
I first heard the words 'group' and 'homomorphism' and 'vector space' in this course, as examples of concrete categories.
I wrote a senior (philosophy) thesis on structuralist philosophy of mathematics.

From 2017-2019 I was a master's student at Carnegie Mellon University, mostly because I was enticed by the work there in homotopy type theory and proof assistants. I took courses on proof theory, automated theorem proving in LEAN, and synthetic homotopy theory.
At CMU I tried to contribute to the program on HoTT, with the help of people like Jonas Frey.
Without much experience with independent research in mathematics, I was not able to successfully complete a master's thesis.

At the moment I am working as an adjunct lecturer at a small engineering school in Boston, where I teach courses in Discrete Math. I enjoy the opportunity to show the virtues of the logical perspective of mathematics to aspiring engineers and programmers.
I can expound at length about the general idea of category theory, but am hopelessly rusty when it comes to actually proving/computing results about it. My hope in joining this community is to have resources and motivation for self-study.

Generally my research interests are epistemic and methodological questions surrounding the practice of pure mathematics.
What is the epistemic role of a proof?
What is the value of 'purely syntactic' reasoning?
When are two formal theories 'equivalent?'
What do we really accomplish when we establish a soundness/completeness result for a formal theory?

I do not know if I plan to pursue further academic research in these areas, but I know that questions like these excite me, as does the ability to address them using formal tools.

Many years ago, I was told that universal and existential quantification can be understood in terms of an adjunction, and for now, understanding that adjunction is my concrete goal.

... I realize my post here is longer than I intended... and despite some attempts to truncate it, I have decided to publish it at it's current length!

John Onstead (Dec 12 2023 at 16:54):

@Adam Millar Welcome to the category theory forum! I'm currently learning categorical logic right now, and it's been helpful for doing so. I look forward to seeing you around here! :)

Todd Trimble (Dec 12 2023 at 21:09):

The series of questions at the end reminded me of an interesting MathOverflow thread, "Is rigour just a ritual that most mathematicians would get rid of if they could?". With regard to the interaction of formal proof with present-day insights of category theory, I want to highlight Andrej Bauer's excellent reply, emphasizing that proofs can be regarded as genuine mathematical objects, no less than numbers are mathematical objects.

Todd Trimble (Dec 12 2023 at 21:09):

Tom Hirschowitz (Dec 13 2023 at 07:50):

Interesting indeed, thanks Todd. It's nice to see @Andrej Bauer emphasise the importance of reconciling truth and explanation in proof theory. Something that puzzles me is his questioning of the “dogma” that proofs can only be finite syntactic entities. Although proofs have models in semantic categories like infinite-categories, I don't think I've ever seen them defined in a non-syntax-like way. Do you fully understand what he means?

Todd Trimble (Dec 13 2023 at 12:22):

John Baez (Dec 13 2023 at 14:36):

For example the language

L(\kappa,\lambda)

discussed here allows conjunctions and disjunctions of collections of formulae of cardinality

< \kappa

, and quantifications over

< \lambda

variables, where

\kappa,\lambda

are cardinals.

John Baez (Dec 13 2023 at 14:37):

In Kanamori's book The Higher Infinite he describes how these infinitary languages are used to study... yes, infinite cardinals! :crazy:

John Baez (Dec 13 2023 at 14:38):

But I think the proofs used here, while infinitely "wide" (since they involve infinitely long formulae) are still only finitely "long" (with finitely many steps).

Mike Shulman (Dec 13 2023 at 16:46):

Most of what I've seen about infinitary logic has been about its models, rather than about its proof theory. If one were going to write down a proof system for infinitary logic, it seems to me that it would be hard to escape infinitely "deep" proofs at least. For instance, a proof of

\bigwedge_{i\in I} \phi_i

should consist of a proof of

\phi_i

for each

i\in I

, and it seems unlikely that it would be possible to impose a uniform bound on the length of those proofs.

Mike Shulman (Dec 13 2023 at 16:48):

"Ill-founded" proofs with infinitely long branches are a different question, but I'd be surprised if someone somewhere hasn't studied them.

John Baez (Dec 13 2023 at 21:04):

Indeed. I've seen work on Turing machine computations that take a nonstandard natural number of steps, but that's a bit different.

Emilio Minichiello (Feb 06 2024 at 15:19):

Hello! I am Emilio, I'm a math PhD student at the CUNY Graduate Center and I'll be finishing up real soon. For my PhD I studied diffeological spaces using higher stacks. I work part-time at Conexus, doing research related to categorical database theory. I want to be more involved in growing the NYC category theory community and maybe reviving this zulip thread could help with that!

Morgan Rogers (he/him) (Feb 06 2024 at 15:24):

Ibrahim Tencer (Feb 12 2024 at 10:17):

Hi everyone, my name is Ibrahim Tencer. I studied pure math at the University of Michigan and have been doing independent research in areas related to socionics, a personality typology that has connections to cybernetics, logic, and quantum information. This is a kind of applied math that has strong ties to category theory (linear logic, Chu spaces, etc.).

You can also find me on Twitter (@sedecology) and Mathstodon (@ibrahimtencer@mathstodon.xyz).
I've written a short introduction to socionics for mathematicians on Mathstodon here: https://mathstodon.xyz/@ibrahimtencer/111693172821994262

Patrick Nicodemus (Feb 12 2024 at 14:30):

Morgan Rogers (he/him) (Feb 12 2024 at 14:39):

This is a very frosty reception @Patrick Nicodemus ! I don't disagree with you, but I worry that this kind of reaction to a self-introduction could be off-putting to other newcomers. (I appreciate that this may be hypocritical considering my recent message on the CT mailing list, but this space is managed a little differently to that one.)

Ibrahim Tencer (Feb 12 2024 at 15:41):

Yes, a few years ago someone decided to put the word "pseudoscience" into the socionics wikipedia article (and wikipedia is never wrong, right?). Whether it is or is not is a discussion we can have, in fact I am working on an article explaining the verification status of socionics that will hopefully clear things up. But in any case, socionics has nontrivial mathematical content regardless of whether it is empirically verified, much like other topics like string theory.

Théo Tyburn (Feb 28 2024 at 19:24):

Hi everyone! :wave:
I'm Théo Tyburn, I study math at master level at Technical University Berlin in Germany. I am interested in applied category theory. My goal is to to learn as much as possible about it during my Master. - the introductory books out there are really good and I'm having fun learning! :octopus:
I would be very interested in doing my Master Thesis on the topic with one of you people as nobody really does this here in Berlin. :handshake:

Ralph Sarkis (Feb 28 2024 at 19:38):

:wave: If you are looking to stay in Germany, there is a good amount of category theorists in the TCS group in Nuremberg.

Stelios Tsampas (Mar 01 2024 at 18:33):

That's true, and some of us (e.g. myself, @Sergey Goncharov, @Henning Urbat , @Lutz Schröder) are members of the CT Zulip community.

Yutaka Miata (Mar 02 2024 at 01:46):

Hi, my name is Yutaka Maita.
I'm a graduate student at Kyoto University in Japan. I study categorical logic, whose relationship to Nonstandard Analysis especially interests me and is also the topic of my master's thesis.
If you have a curiosity about such a thing, talk with me!

JR Learnstomath (Mar 15 2024 at 05:57):

Hi! :wave: I'm a first year student doing maths at Open University UK. I discovered category theory in 2020 and have been self-studying on the side for 2 years now and loving it. I'm interested in applying it to dynamical systems with different degrees of "maybeness", specifically how humans learn (individually and together), and how they work with electronics to organize and make sense of what they know/discover. :brain: :silhouettes: :computer: I'm here thanks to @Owen Lynch and @David Egolf 's kindness and nudges -- after 2 years I'm still not too far away from the absolute beginner mark, so I wasn't sure about whether it was okay to join. I'm really excited to be in a space with the authors of works/videos I've been studying/watching, and I'd love to one day do a PhD that applies category theory.

Paul Wang (Apr 16 2024 at 11:57):

Hi ! I'm a PhD student from Paris, in model theory of valued fields (a mix of algebra and mathematical logic). I discovered category theory 6 years ago, always found it interesting. Until recently, I wasn't aware of all the potential applications (outside of pure maths, I mean) !
I would like to work in that field in the future; I am currently learning about categorical systems theory.

Gregory Chichery (Jun 21 2024 at 14:49):

Hi ! I'm Gregory Chichery, PhD student at Marseille. My subject is semantics of circular proof so I investigate lot of questions about monoidal closed, star-autonomous categories, (co)algebras and recently I am interested about enriched categories.
Looking forward to talking with you !

Hasith Vattikuti (Jul 15 2024 at 20:57):

Hello! I’m Hasith, a physics and mathematics student at the University of Texas at Austin, and I’m excited to learn about category theory and try to apply it to theoretical ML. I’m currently going through seven sketches in compositionality to gain some good footing in act

Feel free to talk to me about anything physics/math/ml related, I’m always happy to learn something new!

Roy Ferguson (Jul 24 2024 at 15:09):

Hello! I am Roy and I am busy with my PhD at Stellenbosch University in South Africa. I am very excited to meet and learn from members of the community!

I'm primarily studying extensivity/distributivity in a monoidal setting. I'm also looking at a Grothendieck fibrations approach to Grothendieck topologies. I am currently introducing myself to topos theory, type theory, fibred category theory, categorical logic, and boolean categories. More broadly I'd like to learn about the different approaches to formal semantics of programming languages and possible connections between these and what I do. I like computers :robot:

All in all, I am very happy to be studying category theory since it feels like it equips you with a toolbox that is useful in many other areas.

Sascha Haupt (Aug 13 2024 at 21:31):

Hi, my name is Sascha. I am a master student in physics, just starting my research about the description of measurement and decoherence in quantum theory by categorical / graphical symplectic algebra.

I'm also interested in philosophy, especially the philosophy of physics and in quantum logic and it's categorical representations.

Another side interest of mine is how to tackle the climate crisis and how math, science and philosophy can contribute to this extraordinarily important task.

John Onstead (Aug 14 2024 at 00:18):

That sounds really cool! As someone who is very interested in both quantum mechanics and category theory, I'm really curious about how to go about doing something like this. So if you have any more details I'd like to hear about it!

Sascha Haupt (Aug 14 2024 at 11:42):

If you are interested in the applications of category theory to quantum mechanics in general, there are different approaches: One ist to look at the

\dag

-compact category Hilb (FHilb) of (finite dimensional) Hilbert spaces, with the monoidal product given by the tensor product. This is the program of categorical quantum mechanics (see also here).

Another approach is so called "topos quantum theory" where one looks at the category of presheaves on the C*-algebra or von Neumann algebras of operators on a given Hilbert space, which form a topos.

My project, which i am just starting with, is about yet another approach, probably more closely related to the former of the above mentioned approaches. The idea is to use subcategories of Rel, along the lines of this paper.

Speaking about quantum logic, there are different approaches as well. The main difference is that, coming from classical (boolean) logic, you either drop distributivity or the law of excluded middle (lem).
Dropping distributivity leads to what is traditionally known as "quantum logic" and goes back to Birkhoff and von Neumann (1936). This version of quantum logic is more closely related to (monoidal) categorical quantum mechanics.
Another approach is to use the internal logic of the aforementioned Bohr topos, which is a Heyting algebra and therefore is distributive, but lem does not hold in this logical system.

John Baez (Aug 14 2024 at 12:00):

Hi! By the way, an annoying feature of this forum is that you need double dollars to get math symbols to work: you wrote $\dag$ but double dollars would give you

\dag

John Baez (Aug 14 2024 at 12:01):

John Onstead (Aug 14 2024 at 21:08):

Thanks for the introduction I'll have to check out all those sources. It seems the first way presented of doing QM in CT is just the direct way- to do the usual Hilbert space formulation of QM, but just in the categorical setting of the category of Hilbert Spaces. But the interesting thing here is that many phenomena of QM seem to remain even when you abstract away to the more general setting of dagger compact categories. The other ways seem to leverage the notion of categories, especially toposes, having an "internal language" or "internal logic" to encapsulate stuff about quantum mechanics.

James Gilles (Sep 06 2024 at 03:55):

Hello, I'm James! I'm a compiler engineer and math hobbyist living in Detroit, Michigan. I like combinatorics and graphics. Here is a picture I drew today:
IMG_20240905_232729_1.jpg

My long-term hobby project is making a WYSIWYG proof assistant. Big fan of the work of people on here, had this zulip bookmarked for a while and thought I should say hi :)

Riley Shahar (Oct 18 2024 at 14:58):

Hey! I'm Riley, a first year PhD student at Penn. I'm definitely in a place where all kinds of math interests me (coming from a small liberal arts college, being at a big research institution in a university town is like a "mathematical candy store" in the words of one of my professors), but I guess right now I'm most likely to go into algebraic topology or categorical logic. I'm also very interested in applications of category theory to cs (semantics of programming languages/etc).

Patrick Nicodemus (Oct 18 2024 at 15:06):

Hi Riley. I'm Patrick and I think we have met a few times at the PL seminar. It's nice to run into you on here.

Stream: community: general

Topic: Introduce yourself!

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