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arXiv · 1910.06094

Davydov-Yetter cohomology, comonads and Ocneanu rigidity

Azat M. Gainutdinov·Jonas Haferkamp·Christoph Schweigert
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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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BibTeXRIS

Azat M. Gainutdinov, Jonas Haferkamp, Christoph Schweigert. 2019-10-14. Davydov-Yetter cohomology, comonads and Ocneanu rigidity. https://doi.org/10.1016/j.aim.2022.108853

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