Universidad de los Andes, Carrera 1 N. 18A - 10, Bogotá, Colombia '
author:
- 'Eugenia Bernaschini, César Galindo and Martín Mombelli'
title: 'Group actions on 2-categories'
---

Introduction {#introduction .unnumbered}
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The theory of 2-categories appears in a natural way in diverse contexts. For example, it was used by Rouquier to “categorify” certain algebraic objects [@R] and appears in topological field theories [@FSV], [@NS]. The theory of representations of 2-categories has been initiated in a series of papers [@MM1; @MM2; @MM3].

Our motivation for the study of 2-categories comes from the theory of tensor categories. For a tensor category ${{\mathcal C}}$, a representation of ${{\mathcal C}}$, or ${{\mathcal C}}$-module category, is a category ${{\mathcal M}}$ equipped with an associative action ${{\mathcal C}}\times {{\mathcal M}}\to {{\mathcal M}}$ satisfying certain conditions. Given two ${{\mathcal C}}$-module categories ${{\mathcal M}}, {{\mathcal N}}$, the category ${\operatorname{Fun}}_{{\mathcal C}}({{\mathcal M}},{{\mathcal N}})$ is the category whose objects are ${{\mathcal C}}$-module functor between ${{\mathcal M}}$ and ${{\mathcal N}}$, and morphisms are ${{\mathcal C}}$-module natural transformations. The 2-category of (left) ${{\mathcal C}}$-modules ${{}_{{{\mathcal C}}}\rm{Mod}}$ has as 0-cells ${{\mathcal C}}$-module categories, 1-cells ${{\mathcal C}}$-module functors between them and 2-cells are ${{\mathcal C}}$-module natural transformations. This 2-category is a strong invariant 