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Chad Nester (Feb 11 2024 at 16:09):Hello everyone,
I've got a few new papers to advertise.
First, Protocol Choice and Iteration for the Free Cornering, together with @Niels Voorneveld. This extends the free cornering of a monoidal category to support additional protocol types, in particular branching protocols, in which one of the participants chooses which of two continuations will happen and the other must respond, and iterated protocols, in which the participants repeat all or part of a protocol some number of times, based on choices made during the process. If you have access to JLAMP you can get the "official" version, but frankly I think the preprint is more legible.
Chad Nester (Feb 11 2024 at 16:12):Second, my PhD thesis, Partial and Relational Algebraic Theories has been successfully defended and is available from the university library. The thesis is a more careful development of the partial algebraic theories and relational algebraic theories from my published work.
I'll mention that only the first ~150 pages of the document on that website are the thesis monograph, with the rest being copies of my papers. It isn't that scary!
Evan Patterson (Feb 11 2024 at 20:04):Congrats on the nice looking thesis! You should post it to arXiv (minus the copied papers). That will help people find it.
Matteo Capucci (he/him) (Feb 12 2024 at 07:58):Congrats!
Chad Nester (Feb 12 2024 at 10:13):Evan Patterson said:
Congrats on the nice looking thesis! You should post it to arXiv (minus the copied papers). That will help people find it.
I don't know whether or not I should do this. I'm planning to publish journal version of the two associated conference papers at some point using material from the thesis, so it might be better to wait. I don't really know.
Kevin Arlin (Feb 12 2024 at 21:20):What downside are you envisioning?
Mike Shulman (Feb 12 2024 at 21:32):I don't know what Chad is thinking, but my own thesis is put together from several papers, and I never put my thesis itself on the arXiv because I would rather that people read the papers instead, as they are more polished. However, this only works if the individual papers actually do get written.
Chad Nester (Apr 17 2024 at 15:31):Tomorrow at 14:00 EEST (UTC+3) I'm giving a talk in Tallinn titled Elgot Categories and Abacus Programs. The talk will be broadcast via Zoom, and if you're interested in listening in send me a message here and I'll send you the details.
Abstract:
This talk concerns the categorical representation of the partial
recursive functions. Specifically, I will introduce Elgot
categories, which are a sort of structured rig category in which
all partial recursive functions are representable. Specifically, an
Elgot category is a (uniform) traced cocartesian rig category
with a distinguished isomorphism I+N→N for some object N.
I will construct an initial Elgot category, the morphisms of
which will coincide with the abacus programs of Lambek. Finally,
I will show that in this initial Elgot category, the class of
strongly representable partial functions is precisely the class
of partial recursive functions.
Chad Nester (Apr 17 2024 at 15:34):I guess the main references are:
Chad Nester (May 13 2024 at 13:18):Today is my first day at my new job as a Research Fellow at the University of Tartu. It's a permanent position, which is exciting.