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Owen Lynch (Mar 24 2022 at 23:48):I'm reading "Information-theoretic foundations of thermodynamics in general probabilistic theories", which is Carlo Maria Scandolo's PhD thesis, and it discusses operational probabilistic theories from (what I as a category theorist) would say is an informal perspective. Other papers that I've looked at on the subject have a similar lack of formalization. Is there any treatment that you all know of that pins down exactly what type of category an operational probabilistic theory is? And also writes down what would be functors between such theories?
Joe Moeller (Mar 25 2022 at 00:41):Would Markov categories be a good starting point? what else would you want it to have?
Sam Staton (Mar 25 2022 at 13:06):Carlo Maria's thesis is nice and I think it's an interesting area. You could also look at Sean Tull's thesis, which is also about operational probabilistic theories but more categorical. https://www.seantull.uk/
@Joe Moeller I guess one could indeed try to make a connection with (say) Arthur Parzygnat's quantum Markov categories.
Owen Lynch (Mar 25 2022 at 19:38):OK, neat, yeah Sean Tull's thesis is what I was looking for