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Nima Rasekh (Aug 06 2025 at 18:16):Hello y'all!
I am considering organizing a seminar on ACT (applied category theory) for Bachelor students, meaning having students give talks on different papers. As part of that I am trying to gather a list of ACT papers with various applications throughout science (physics, chemistry, biology, computer science, anything).
The main challenge I face is that I need (at least some) papers that require very little category theory background, given that some students don't have a signficant experience.
@David Corfield suggested asking on Zulip, whether anybody has a suggestion how to find papers, which involve different levels of category theory (ranging from mostly using the basic definitions up to advanced categorical concepts).
Any suggestion would be much appreciated!
Kevin Carlson (Aug 06 2025 at 18:33):Spivak and Kent's original paper on ologs was written to have basically no prerequisites, I think, and it's also can serve as the key marker for when the modern field of ACT got started.
Nima Rasekh (Aug 06 2025 at 18:36):Kevin Carlson said:
Spivak and Kent's original paper on ologs was written to have basically no prerequisites, I think, and it's also can serve as the key marker for when the modern field of ACT got started.
Seems fun, thanks a lot!
Ralph Sarkis (Aug 06 2025 at 18:57):You can look into the papers that were listed for the various ACT adjoint school projects.
Nima Rasekh (Aug 06 2025 at 18:59):Thank @Ralph Sarkis !
Yes, @David Corfield did already suggest this (along with Zulip) and I forgot mentioning that, so I am planning on checking those sources out more carefully, but of course it can't hurt to ask for additional papers!
David Corfield (Aug 06 2025 at 19:31):If you were open to considering a book to work through, you might look at
Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory
accompanied by John Baez's associated lectures.
Nima Rasekh (Aug 06 2025 at 19:47):David Corfield said:
If you were open to considering a book to work through, you might look at
Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory
accompanied by John Baez's associated lectures.
Thanks a lot! That has a lot of cool topics, in fact the first chapters seem reasonably accessible.
John Baez (Aug 06 2025 at 20:26):Here's a self-contained expository article on a nice application of category theory to language processing:
Nima Rasekh (Aug 06 2025 at 20:33):John Baez said:
Here's a self-contained expository article on a nice application of category theory to language processing:
- Tai-Danae Bradley, Juan Luis Gastaldi and John Terilla, The structure of meaning in language: parallel narratives in linear algebra and category theory.
Looks interesting, thanks @John Baez ! Gotta now learn some linguistics.
Peter Arndt (Aug 12 2025 at 14:00):Here are some references which I offered for a similar seminar back in 2022. I was pushing students a bit towards uses of category theory in probability theory and data science.
Nima Rasekh (Aug 12 2025 at 14:31):Peter Arndt said:
Here are some references which I offered for a similar seminar back in 2022. I was pushing students a bit towards uses of category theory in probability theory and data science.
Heyho @Peter Arndt that's very cool and well thought out. From the plan it seems to me you had some pretty decent students. How did this go, did you get students to enjoy category theory?
Peter Arndt (Aug 12 2025 at 15:19):It went ok! This was for our master program in AI and Data Science, which is open to all kinds of people with a STEM bachelor, so not all were mathematicians. E.g. I had a biologist and a cognitive scientist in that class who gave quite decent talks.
I gave three introductory lectures myself, on categories/(co)limits and such basics, and on monoidal categories via string diagrams. The seminar was small enough that I could grab some talks for myself, and I felt that the foundation was the most important part. I gave some live exercises, and I had the impression that people were ok with handling string diagrams after my talks.
Then we had student talks on entropy, graphical linear algebra, causality, backprop as a functor, Spivak's data migration via Kan extensions, categorical probability (including the categorical proof of the 0-1 law).
I think each student enjoyed thinking through their topic of choice in categorical terms. But I am not sure it bought them much for their further studies.
In hindsight I think the collection of topics was a bit too scattered for that. If I offer this seminar again, I probably would narrow down the collection of topics to just things from categorical probability and entropy. I imagine that the students would then have a better chance to really adopt the categorical point of view on this one topic (categories of stochastic maps) and be able think in those terms later on in their "real life".
But I think this is due to the particular situation of our AI students, who do a lot of applied stuff, where categorical points of view don't suggest themselves that naturally. If you run this seminar for math students, they will have plenty of opportunity to think categorically about all kinds of math later, so scattered topics wouldn't be that much of a problem, I imagine.
Nima Rasekh (Aug 12 2025 at 20:01):Peter Arndt said:
It went ok! This was for our master program in AI and Data Science, which is open to all kinds of people with a STEM bachelor, so not all were mathematicians. E.g. I had a biologist and a cognitive scientist in that class who gave quite decent talks.
I gave three introductory lectures myself, on categories/(co)limits and such basics, and on monoidal categories via string diagrams. The seminar was small enough that I could grab some talks for myself, and I felt that the foundation was the most important part. I gave some live exercises, and I had the impression that people were ok with handling string diagrams after my talks.
Then we had student talks on entropy, graphical linear algebra, causality, backprop as a functor, Spivak's data migration via Kan extensions, categorical probability (including the categorical proof of the 0-1 law).
I think each student enjoyed thinking through their topic of choice in categorical terms. But I am not sure it bought them much for their further studies.
In hindsight I think the collection of topics was a bit too scattered for that. If I offer this seminar again, I probably would narrow down the collection of topics to just things from categorical probability and entropy. I imagine that the students would then have a better chance to really adopt the categorical point of view on this one topic (categories of stochastic maps) and be able think in those terms later on in their "real life".But I think this is due to the particular situation of our AI students, who do a lot of applied stuff, where categorical points of view don't suggest themselves that naturally. If you run this seminar for math students, they will have plenty of opportunity to think categorically about all kinds of math later, so scattered topics wouldn't be that much of a problem, I imagine.
This sounds very amazing, and very much close to the platonic ideal of the event I imagined.
I think in my case the students would be a mix of Math and Math/CS Bachelor students, so I would have to start from a lower level. But very happy to hear your event was this succesful, makes me more optimistic. It is funny, I myself was already thinking (and very much unsure) about picking between a "scattered seminar" vs. "guided seminar", so it's interesting you struggled with the same issue.