Invariants and semi-direct products for finite group actions on tensor categories. (English) Zbl 0980.18003

Given an action of a finite group on a tensor category, we form two tensor categories. One is the category of group invariant objects of the tensor category, and the other is the semi-direct product of the group and the tensor category. We show that if the characteristic of the base field does not divide the order of the group, there exists a one-to-one correspondence between linear categories with action of these two tensor categories.
Reviewer: D.Tambara


18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
20J06 Cohomology of groups
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
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