| We define a notion of tensor product of bimodule categories and prove that with this product the 2-category of C -bimodule categories for fixed tensor C is a monoidal 2-category in the sense of Kapranov and Voevodsky ([KV91]). We then provide a monoidal-structure preserving 2-equivalence between the 2-category of C -bimodule categories and Z( C )-module categories (module categories over the center of C ). The (braided) tensor structure of C1⊠D C2 for (braided) fusion categories over braided fusion D is introduced. For a finite group G we show that de-equivariantization is equivalent to the tensor product over Rep( G). The fusion rules for the Grothendeick ring of Rep(G)-module categories are derived and it is shown that the group of invertible Rep( G)-module categories is isomorphic to H2 (G, kx), extending results in [ENO09]. |
