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

Davydov-Yetter cohomology, comonads and Ocneanu rigidity