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abstract: 'We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups. Associated to a group action on a 2-category, we construct the 2-category of equivariant objects. We also introduce the $G$-equivariant notions of pseudofunctor, pseudonatural transformation and modification. Our first main result is a coherence theorem for 2-categories with an action of a group. For a 2-category ${{\mathcal B}}$ with an action of a group $G$, we construct a braided $G$-crossed monoidal category $\mathcal{Z}_G({{\mathcal B}})$ with trivial component the Drinfeld center of ${{\mathcal B}}$. We prove that, in the case of a $G$-action on the 2-category of representation of a tensor category ${{\mathcal C}}$, the 2-category of equivariant objects is biequivalent to the module categories over an associated $G$-extension of ${{\mathcal C}}$. Finally, we prove that the center of the equivariant 2-category is monoidally equivalent to the equivariantization of a relative center, generalizing results obtained in [@GNN].'
address:
- 'Facultad de Matemática, Astronomía y Física Universidad Nacional de Córdoba CIEM – CONICET Medina Allende s/n (5000) Ciudad Universitaria, Córdoba, Argentina'
- ' Departamento de Matemáticas, 