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Hochschild-Mitchell cohomology and Galois extensions

Estanislao Herscovich·Andrea Solotar
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Abstract

We define $H$-Galois extensions for $k$-linear categories and a Hopf algebra $H$ and prove the existence of a Grothendieck spectral sequence for Hochschild-Mitchell cohomology, related to this situation. This spectral sequence is multiplicative and for a $H$ a group algebra decomposes as a direct sum indexed by the set of conjugacy classes of the group. We also compute some Hochschild-Mitchell cohomology groups of categories with infinite associated quiver.

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Estanislao Herscovich, Andrea Solotar. 2005-10-07. Hochschild-Mitchell cohomology and Galois extensions. https://arxiv.org/abs/math/0510160

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