  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.
