Davydov-Yetter cohomology, comonads and Ocneanu rigidity

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