We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category C to be equivalent. This concludes the classification of such ...

Let (Formula presented.) be a modular category of Frobenius-Perron dimension dqn, where q > 2 is a prime number and d is a square-free integer. We show that (Formula presented.) must be integral and nilpotent and therefore ...

For a finite tensor category C and a Hopf monad T : C --> C satisfying certain conditions we describe exact indecomposable left C^T-module categories in terms of left C-module categories and some extra data. We also give ...

We describe equivalence classes of indecomposable exact module categories over a finite graded tensor category. When applied to a pointed fusion category, our results coincide with the ones obtained in [11].

We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. ...

We develop further the techniques presented in a previous article (M. Mombelli. Abh. Math. Semin. Univ. Hamb. 82 (2012), 173–192), to study bimodule categories over the representation categories of arbitrary finite-dimensional ...

For any finite-dimensional Hopf algebra H we construct a group homomorphism BiGal (H) → BrPic(Rep(H)), from the group of equivalence classes of H-biGalois objects to the group of equivalence classes of invertible exact ...

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 ...

We generalize the notion of ends and coends in category theory to the realm of module categories over finite tensor categories. We call this new concept module (co)end. This tool allows us to give different proofs to several ...