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Extensions of tensor categories by finite group fusion categories

Extensions of tensor categories by finite group fusion categories

Abstract We study exact sequences of finite tensor categories of the form Rep G โ†’ ๐’ž โ†’ ๐’Ÿ, where G is a finite group. We show that, under suitable assumptions, there exists a group ฮ“ and mutual actions by permutations โŠณ : ฮ“ ร— G โ†’ G and โŠฒ : โ€ฆ