An outline of some ideas we had lately on the problem of dependent optics, including some solutions.

Twitter thread.

MSP101 introductory talk about optics, focusing in profunctor optics. I also made the notes of the talk into a blog post.

Talk about the Para and Proxy constructions. A companion paper is in the workings.A recording is available here.

Distinguished talk about the eponymous paper.

An invitation to some new and old mathematical gadgets and their use to model cybernetic systems, including but not limited to open games and machine learning.

We show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion of player and their agency within open games, and the lack of choice operators. Using the former we construct the latter, and these choice operators subsume previous proposed operators for open games, thereby making progress towards a core, canonical and ergonomic calculus of game operators. Collectively these innovations increase the level of compositionality of open games, and demonstrate their expressiveness.

An MSP101 talk about recent developments in the theory of open games, with some speculations about the role of the new machinery for categorical cybernetics.

A TallCat seminar about my master thesis and follow up work. I shows how some notions of stochastic calculus can be internalized in a sheaf topos. Full abstract and recording at the above link.