论文标题
关于G跨编织类别的三类观点
A 3-categorical perspective on G-crossed braided categories
论文作者
论文摘要
编织的单体类别可以被视为一个$ 3 $类别，其中一个对象和一个$ 1 $塑料。在本文中，我们表明，更一般而言，具有一个对象的$ 3 $类别，由$ g $的元素给出的$ 1 $的跨性别对应于$ g $ - 跨性的编织类别，某些数学结构已成为重要的低维量子场理论的重要不变性。更准确地说，我们表明，配备了3件功能的$ \ m atrm {b} g \ to \ mathcal {c} $的4类，$ 3 $ - 类别$ \ mathcal {c} $，本质上是$ 1 $ -morphisms的类别，与$ 2 $ -2 $ -CATEROSS相等。这为$ g $涂的编织类别的各种结构提供了统一的方法。
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 $G$ 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.
