Rigid commutative algebras and a generalized 1D cobordism hypothesis

Abstract: Baez and Dolan's cobordism hypothesis, in dimension 1, describes the free symmetric monoidal infinity-category on a dualizable object as a certain cobordism category. It's only reasonable to try and guess what a generalization of this may look like, namely how one could describe free rigid categories on more complicated inputs.

In this talk, I will explain how a generalization of the notion of "rigid category" to other settings leads to a proof of the natural guess by bootstrapping from the usual cobordism hypothesis. This generalization, namely the notion of rigid commutative algebra in a symmetric monoidal (∞,2)-category, has received growing attention following recent advances in algebraic K-theory, and I will spend some time discussing it.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)