  We prove Eilenberg-Watts Theorem for 2-categories of the representation
categories $\C\x\Mod$ of finite tensor categories $\C$. For a consequence we
obtain that any autoequivalence of $\C\x\Mod$ is given by tensoring with a
representative of some class in the Brauer-Picard group $\BrPic(\C)$. We
introduce bialgebroid categories over $\C$ and a cohomology over a symmetric
bialgebroid category. This cohomology turns out to be a generalization of the
one we developed in a previous paper and moreover, an analogous
Villamayor-Zelinsky sequence exists in this setting. In this context, for a
symmetric bialgebroid category $\A$, we interpret the middle cohomology group
appearing in the third level of the latter sequence. We obtain a group of
quasi-monoidal structures on the representation category $\A\x\Mod$.
