The monoidal centre for group-graded categories

Ross Street – 1 July 2020

Let G be a group and k be a commutative ring. Our aim is to ameliorate the G-graded categorical structures considered by Turaev and Virelizier by fitting them into the monoidal bicategory context.

We explain how these structures are monoidales in the monoidal centre of the monoidal bicategory of k-linear categories on which G acts. This provides a useful example of a higher version of Davydov's full centre of an algebra.