  Davydov-Yetter cohomology classifies infinitesimal deformations of tensor
categories and of tensor functors. Our first result is that Davydov-Yetter
cohomology for finite tensor categories is equivalent to the cohomology of a
comonad arising from the central Hopf monad. This has several applications:
First, we obtain a short and conceptual proof of Ocneanu rigidity. Second, it
allows to use standard methods from comonad cohomology theory to compute
Davydov-Yetter cohomology for a family of non-semisimple finite-dimensional
Hopf algebras generalizing Sweedler's four dimensional Hopf algebra.
