Résume | Fusion categories arise in several areas of mathematics- such as the representation theory of Hopf algebras and topological quantum field theory. They are tensor categories which satisfy certain rigidity assumptions- they are semisimple, have a finite number of simple objects, and they have duals. A general classification of fusion categories seems to be out of reach at the moment. However, Etingof Nikshych and Ostrik have classified all fusion categories which are extensions of a given fusion category by a given finite group $G$, by cohomological machinery (these are categories which are naturally graded by the group $G$) In this talk I will describe a joint work with Evgeny Musicantov, about the classification of module categories (which, in this setting, are the categorical analogues of modules over a ring) over these fusion categories. I will explain all the fundamental notions, their relevance for the theory of Hopf algebras, and the role that the cohomological machinery plays in the classification. |