BIMSA > BIMSA TQFT and Higher Symmetries Seminar Tannaka-Krein reconstruction for fusion 2-categories
Tannaka-Krein reconstruction for fusion 2-categories
Organizers
Ansi Bai , Chun Chen , Liang Kong , Yi Long Wang , Zhi Hao Zhang , Hao Zheng
Speaker
David Green
Time
Tuesday, October 15, 2024 9:40 AM - 11:10 AM
Venue
A3-2-301
Online
Zoom 361 038 6975 (BIMSA)
Abstract
Tannaka-Krein reconstruction is a well known procedure which recovers a Hopf algebra from its category of modules and monoidal fiber functor. Following the approach of P. Schauenburg, we show how to recover a semisimple Hopf monoidal category from its fusion 2-category of representations. Next, we provide a complete classification of Hopf categories following work of T. Décoppet and M. Yu. If time permits, I will also provide some remarks on in-progress work on a more general reconstruction theorem applicable to any symmetric fusion 2-category.