A 3‐categorical perspective on G$G$‐crossed braided categories
A 3‐categorical perspective on G$G$‐crossed braided categories
复制标题
G$G$ 的 3 类别视角 — 交叉编织类别
DOI：
10.1112/jlms.12687
复制
发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Reutter, David
中科院分区：
文献类型：
--
作者：
Jones, Corey;Penneys, David;Reutter, David
辫状幺半群范畴可以被认为是具有一个对象和一个 1-态射的 3-范畴。在本文中，我们证明，更一般地，由群 G$G$ 的元素给出的具有一个对象和 1-态射的 3-范畴对应于 G$G$-交叉编织范畴，某些数学结构已成为低维量子场论的重要不变量。更准确地说，我们证明了配备有 3-函子 BG→C$\mathrm{B}G \rightarrow \mathcal {C}$ 的 3-范畴 C$\mathcal {C}$ 的 4-范畴，其本质上是对象上的满射和 1-态射，相当于 G$G$交叉编织范畴的 2-范畴。这为 G$G$ 交叉编织类别的各种构造提供了统一的方法。
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$G$ correspond to G$G$‐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 C$\mathcal {C}$ equipped with a 3‐functor BG→C$\mathrm{B}G \rightarrow \mathcal {C}$ which is essentially surjective on objects and 1‐morphisms is equivalent to the 2‐category of G$G$‐crossed braided categories. This provides a uniform approach to various constructions of G$G$‐crossed braided categories.