On Morita equivalence of pointed fusion categories

Pointed fusion categories are characterized by a finite group and a 3-cocycle with values in U(1). In this talk I will show under which necessary and sufficient conditions two pointed fusion categories have equivalent categories of modules. Since Morita equivalent  pointed fusion categories have isomorphic Drinfeld centers, we obtain as a byproduct isomorphic Drinfeld doubles associated to different groups and different 3-cocycles.