Module categories over equivariantized tensor categories

Abstract

For a finite tensor category $\mathcal{C}$ and a Hopf monad $T:\mathcal{C}\to \mathcal{C}$ satisfying certain conditions we describe exact indecomposable left ${\mathcal{C}}^T$-module categories in terms of left $\mathcal{C}$-module categories and some extra data. We also give a 2-categorical interpretation of the process of equivariantization of module categories.

33 pages, amslatex