Monoidal 2-structure of Bimodule Categories

Details Monoidal 2-structure of Bimodule Categories Monoidal 2-structure of Bimodule Categories

2009-11-25

arxiv.org/abs/0911.4979v4

Mathematics

Quantum Algebra

40 pages, minor errors corrected, references added. To appear in J. Algebra

Scientific paper

10.1016/j.jalgebra.2010.06.018

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. 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). For finite group G we show that de-equivariantization is equivalent to tensor product over category Rep(G) of finite dimensional representations. We derive Rep(G)-module fusion rules and determine the group of invertible irreducible Rep(G)-module categories extending earlier results for abelian groups.

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