北京雁栖湖应用数学研究院

黄林哲 , 刘正伟 , Sébastien Palcoux , 王亦龙 , 吴劲松

David Penneys

2022年11月09日 09:00 至 10:30

1131

Zoom 537 192 5549 (BIMSA)

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.