Module Eilenberg-Watts calculus

Understand

The categorical formulation of the Eilenberg-Watts calculus relates, for any pair of finite categories M and N, the finite categories Fun^{le}(N,M) and Fun^{re}(N,M) of linear left or right exact functors and the Deligne product \bar N \boxtimes M by adjoint equivalences.

• We establish a variant of this calculus for the case that the finite categories M and N are module categories over a finite tensor category.
• This provides in particular canonical and explicitly computable equivalences between categories of left or right exact module functors (or, more generally, balanced functors) and certain twisted centers of bimodule categories.