Davydov-Yetter cohomology, comonads and Ocneanu rigidity

Understand

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.