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Abstract: We define a notion of tensor product of bimodule categories and prove thatwith this product the 2-category of C-bimodule categories for fixed tensor C isa monoidal 2-category in the sense of Kapranov and Voevodsky. We then provide amonoidal-structure preserving 2-equivalence between the 2-category ofC-bimodule categories and ZC-module categories module categories over thecenter. For finite group G we show that de-equivariantization is equivalent totensor product over category RepG of finite dimensional representations. Wederive RepG-module fusion rules and determine the group of invertibleirreducible RepG-module categories extending earlier results for abeliangroups.

Autor: Justin Greenough


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