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arXiv · 1910.13557

Drinfeld Centre-Crossed Braided Tensor Categories

Thomas A. Wasserman
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Abstract

We introduce, for a symmetric fusion category $\mathcal{A}$ with Drinfeld centre $\mathcal{Z}(\mathcal{A})$, the notion of $\mathcal{Z}(\mathcal{A})$-crossed braided tensor category. These are categories that are enriched over $\mathcal{Z}(\mathcal{A})$ equipped with a symmetric tensor product, while being braided monoidal with respect to the usual tensor product on $\mathcal{Z}(\mathcal{A})$. In the Tannakian case where $\mathcal{A}=\mathbf{Rep}(G)$ for a finite group $G$, the 2-category of $\mathcal{Z}(\mathcal{A})$-crossed braided categories is shown to be equivalent to the 2-category of $G$-crossed braided tensor categories. A similar result is established for the super-Tannakian case where $\mathcal{A}$ is the representation category of a finite super-group.

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Thomas A. Wasserman. 2019-10-29. Drinfeld Centre-Crossed Braided Tensor Categories. https://arxiv.org/abs/1910.13557

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