K-theory of monoids via double categories

Abstract: For any finite group G, there is a well-known formula that computes the algebraic K-theory of the category of finite G-sets; i.e. finite sets with a G-action. Interestingly, if we drop the existence of inverses and swap G by a monoid M, things get a lot more complicated and each step in the proof independently breaks down!

In this talk, I will explain how we can save the day by considering a double category of M-sets instead. Along the way, I will try to outline some recent developments in algebraic K-theory that make heavy use of double categories.

The talk won't assume any knowledge of K-theory, and will only assume a working understanding of what a double category is.

category theory

Audience: researchers in the topic

Third Virtual Workshop on Double Categories