Categorical interaction in the polynomial ecosystem

Abstract: Category theory offers an elegant, compositional, and well-interoperating framework in which to formalize many different sorts of interacting systems, including database, dynamical, software, learning, and game-playing systems.

In this talk I'll start by giving a bird's-eye view of these applications. I'll then discuss polynomial functors and the associated framed bicategory Cat# of comonoids. I'll say a bit about how Cat# fits into the above stories and spend the remainder of the time trying to give a hint as to the astounding amount of structure this category has.

One might think of Cat# like the complex numbers: simultaneously extremely useful in applications and extremely mathematically well-behaved, the combination of which gives a sense of its being more "part of nature" than "human-made".

category theory

Audience: researchers in the topic

( slides | video )

Intercats: Seminar on Categorical Interaction