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arXiv · 2202.07701

Exact factorizations and extensions of finite tensor categories

Tathagata Basak·Shlomo Gelaki
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Abstract

We extend \cite{G} to the nonsemisimple case. We define and study exact factorizations $\B=\A\bullet \C$ of a finite tensor category $\B$ into a product of two tensor subcategories $\A,\C\subset \B$, and relate exact factorizations of finite tensor categories to exact sequences of finite tensor categories with respect to exact module categories \cite{EG}. We apply our results to study exact factorizations of quasi-Hopf algebras, and extensions of a finite group scheme theoretical tensor category \cite{G2} by another one. We also provide several examples to illustrate our results.

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Tathagata Basak, Shlomo Gelaki. 2022-02-15. Exact factorizations and extensions of finite tensor categories. https://arxiv.org/abs/2202.07701

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