Algebraic K-theory describes how diverse mathematical objects can be built by combining finitely many smaller pieces. To do this rigorously requires definitions of what "combining" and "smaller" mean, and there are several established frameworks that make these notions precise, each accommodating different examples and results. The CGW categories of Campbell and Zakharevich treat complementary inclusions of sets or algebraic varieties in the same way as short exact sequences of modules, where both exhibit an object as a combination of two smaller ones. In joint work with Maru Sarazola, we use this analogy to extend several classical results from the algebraic K-theory of modules to finite sets and varieties. In our main result, we define chain complexes of finite sets and their K-theory, and show that it agrees with the K-theory of finite sets.

There will be a pretalk by Chase Vogeli at 12:20pm.