@twocubes @loving-n0t-heyting The links etc I promised:
The main guy's writeups:
https://arxiv.org/pdf/2509.03780
https://www.lesswrong.com/posts/XHtygebvHoJSSeNPP/some-rules-for-an-algebra-of-bayes-nets
https://www.lesswrong.com/posts/dWQWzGCSFj6GTZHz7/natural-latents-the-math
https://www.lesswrong.com/posts/RTiuLzusJWyepFpbN/why-care-about-natural-latents
My partial writeups:
https://www.overleaf.com/read/wfpkyjhmmwvy#5441d9
https://www.lesswrong.com/collaborateOnPost?postId=TsFaJnxrPx6LWTWSC&key=f7d71ecf3e5b3e9f7354ebce03b521
https://www.lesswrong.com/editPost?postId=nAaLSq5izGn7kZheu&key=9e4531fcb6e0659a4d1bf16e59d9ea
My general plan: Finish up notating the rules for the algebra of Bayes nets in terms of blackbox rewriting rules for monoidal category string diagrams. Use category theory to find any rules JSW might have missed. Use even more category theory to figure out where any useful universal properties fall out, like his sense of isomorphism. Use yet more category theory to talk about this stuff in full generality, not just for Bayes nets, and probably even get cleaner or stronger proofs.
Some keywords that came up: Morita equivalence, Petri net, virtual double category, formal category theory, Lawvere metric spaces
