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arXiv · 2006.08022

Braided Picard groups and graded extensions of braided tensor categories

Alexei Davydov·Dmitri Nikshych
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Abstract

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.

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Alexei Davydov, Dmitri Nikshych. 2020-06-14. Braided Picard groups and graded extensions of braided tensor categories. https://arxiv.org/abs/2006.08022

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