A 3-categorical perspective on G-crossed braided categories
组织者
演讲者
David Penneys
时间
2022年11月09日 09:00 至 10:30
地点
1131
线上
Zoom 537 192 5549
(BIMSA)
摘要
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.