BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar A 3-categorical perspective on G-crossed braided categories
A 3-categorical perspective on G-crossed braided categories
Organizers
Lin Zhe Huang , Zheng Wei Liu , Sébastien Palcoux , Yi Long Wang , Jin Song Wu
Speaker
David Penneys
Time
Wednesday, November 9, 2022 9:00 AM - 10:30 AM
Venue
1131
Online
Zoom 537 192 5549 (BIMSA)
Abstract
A braided monoidal category may be considered a $3$-category with one object and one $1$-morphism. In this paper, we show that, more generally, $3$-categories with one object and $1$-morphisms given by elements of a group $G$ correspond to $G$-crossed braided categories, certain mathematical structures which have emerged as important invariants of low-dimensional quantum field theories. More precisely, we show that the 4-category of $3$-categories $\mathcal{C}$ equipped with a 3-functor $\mathrm{B}G \to \mathcal{C}$ which is essentially surjective on objects and $1$-morphisms is equivalent to the $2$-category of $G$-crossed braided categories. This provides a uniform approach to various constructions of $G$-crossed braided categories. This is joint work with Corey Jones and David Reutter which has just appeared open access at https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12687.