Davydov-Yetter cohomology, comonads and Ocneanu rigidity
arXiv:1910.06094 · doi:10.1016/j.aim.2022.108853
Abstract
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.
45 pages; v2: typos fixed, proof of Cor. 4.8 added, the version for publication in Advances in Mathematics