Braided Picard groups and graded extensions of braided tensor categories
Braided Picard groups and graded extensions of braided tensor categories
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DOI：
10.1007/s00029-021-00670-1
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发表时间：
2020-06
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通讯作者：
A. Davydov;D. Nikshych
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文献类型：
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作者：
A. Davydov;D. Nikshych
我们根据 2 分类皮卡德群对有限编织张量范畴的各种类型的分级扩展进行分类。特别是，我们证明有限群 A 的编织扩张对应于从 A 到编织 2-分类皮卡德群（由可逆中心模范畴组成）的编织幺半 2-函子。此类函子可以用 Eilnberg-Mac Lane 上同调来表示。我们详细描述了对称融合类别和尖编织融合类别的编织 2-分类 Picard 群。
We classify various types of graded extensions of a finite braided tensor categoryin terms of its 2-categorical Picard groups. In particular, we prove that braided extensions ofby a finite groupAcorrespond to braided monoidal 2-functors fromAto the braided 2-categorical Picard group of(consisting of invertible central-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.