Strongly-fusion 2-categories are grouplike

Abstract: A *fusion category* is a finite semisimple monoidal category in which the unit object is indecomposable, equivalently has trivial endomorphism algebra. There are two natural categorifications of this notion: a *fusion 2-category* is a finite semisimple monoidal 2-category in which the unit object is indecomposable, and a *strongly fusion 2-category* is one in which the unit object has trivial endomorphism algebra. As I will explain in this talk, fusion 2-categories are extremely rich, with a seemingly-wild classification, whereas strongly-fusion 2-category are very simple: they are essentially just finite groups. Based on joint work with Matthew Yu.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar