论文标题
编织的PICARD组并分级编排编织的张量类别
Braided Picard groups and graded extensions of braided tensor categories
论文作者
论文摘要
我们根据其$ 2 $分类的PICARD组对有限编织的张量类别$ \ cal b $的各种分级扩展进行了分类。特别是，我们证明有限的组$ a $的编织$ \ cal b $对应于编织的单体$ 2 $ functors，从$ a $到编织的$ 2 $ 2 $ - 类别的PICARD $ \ cal b $（由Increvertible Central $ \ cal b $ -odule类别组成）。这样的函子可以用Eilnberg-Mac〜Lane的同谋表示。我们详细描述编织$ 2 $ - 类别的对称融合类别的PICARD组和尖头编织的融合类别。
We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $\cal B$ by a finite group $A$ correspond to braided monoidal $2$-functors from $A$ to the braided $2$-categorical Picard group of $\cal B$ (consisting of invertible central $\cal B$-module categories). Such functors can be expressed in terms of the Eilnberg-Mac~Lane cohomology. We describe in detail braided $2$-categorical Picard groups of symmetric fusion categories and of pointed braided fusion categories.
