Fusion rules of equivariantizations of fusion categories

Abstract

We determine the fusion rules of the equivariantization of a fusion category $\mathcal{C}$ under the action of a finite group $G$ in terms of the fusion rules of $\mathcal{C}$ and group-theoretical data associated to the group action. As an application we obtain a formula for the fusion rules in an equivariantization of a pointed fusion category in terms of group-theoretical data. This entails a description of the fusion rules in any braided group-theoretical fusion category.

The assumption that the group action is by tensor autoequivalences on a fusion category was added in Section 2. Modified statements of Proposition 6.2, Corollary 2.13. Statements of Propositions 3.12 and Corollary 3.13 modified accordingly

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