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Max New (Oct 24 2022 at 19:41):Dan Licata and I recently posted an article on Arxiv about a logical notation for formal category theory: https://arxiv.org/abs/2210.08663 . There is a cool analogy between predicate logic and concepts in virtual equipments that we use: Screen-Shot-2022-10-24-at-3.39.04-PM.png. This syntax corresponds to virtual equipments + some universal properties, and next steps would be to explore syntax for monoidal closed equipments + duality involutions.
I know several people on here are interested in double categories and formal category theory so I'm happy to discuss.
Jean-Baptiste Vienney (Oct 24 2022 at 20:19):It looks incredibly nice. But I don't know a lot on the subject. Is it necessary to already understand formal category theory to understand your logic or is it possible to understand formal category theory by understanding your logic?
Max New (Oct 24 2022 at 20:25):You can interpret everything in the logic in terms of ordinary categories, we describe the semantics as we go. So in that sense you can use the logic to extend what you know about category theory to formal category theory.
Jean-Baptiste Vienney (Oct 24 2022 at 20:27):Thank you, so, I'll probably do that :)