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Davydov-Yetter cohomology, comonads and Ocneanu rigidity

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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.
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Dates and versions

hal-03099209 , version 1 (06-01-2021)

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Azat M. Gainutdinov, Jonas Haferkamp, Christoph Schweigert. Davydov-Yetter cohomology, comonads and Ocneanu rigidity. 2021. ⟨hal-03099209⟩
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