A 3-categorical perspective on G-crossed braided categories

Speaker: David Penneys (The Ohio State University)

Date:    2022.11.09

Time:   09:00-10:30 am

Zoom: 537 192 5549   Passcode: BIMSA

Venue: BIMSA 1131

 

Abtract:

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.

 

[BIMSA-Tsinghua Quantum Symmetry Seminar]