#### Vol. 7, No. 6, 2013

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The Picard crossed module of a braided tensor category

### Alexei Davydov and Dmitri Nikshych

Vol. 7 (2013), No. 6, 1365–1403
##### Abstract

For a finite braided tensor category $\mathsc{C}$ we introduce its Picard crossed module $\mathfrak{P}\left(\mathsc{C}\right)$ consisting of the group of invertible $\mathsc{C}$-module categories and the group of braided tensor autoequivalences of $\mathsc{C}$. We describe $\mathfrak{P}\left(\mathsc{C}\right)$ in terms of braided autoequivalences of the Drinfeld center of $\mathsc{C}$. As an illustration, we compute the Picard crossed module of a braided pointed fusion category.

##### Keywords
braided tensor category, Drinfeld center, braided autoequivalence, invertible module category
Primary: 18D10
Secondary: 16W30