David Penneys
The Ohio State University
Title
Weak rigidity implies rigidity for finite semisimple braided monoidal categories
Abstract
In this talk, we will give a complete proof that weak rigidity implies rigidity for finite semisimple braided monoidal categories. The proof relies on the fact that every object in such a category has moderate growth, so our results hold in much greater generality. As applications, we get a simplification of Huang's proof of rigidity of representation categories of certain vertex operator algebras, and we get that for a finite semisimple monoidal category C, the data of a C-modular functor is equivalent to a modular fusion category structure on C, answering a question of Bakalov and Kirillov. This is joint work with Pavel Etingof [arXiv:2412.17681].