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Davydov-Yetter cohomology, comonads and Ocneanu rigidity

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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https://hal-univ-tours.archives-ouvertes.fr/hal-03099209
Contributor : Sandrine Renard-Riccetti <>
Submitted on : Wednesday, January 6, 2021 - 9:07:44 AM
Last modification on : Friday, January 8, 2021 - 3:27:37 AM
Long-term archiving on: : Wednesday, April 7, 2021 - 6:32:57 PM

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1910.06094.pdf
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  • HAL Id : hal-03099209, version 1
  • ARXIV : 1910.06094

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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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