Hochschild-Mitchell cohomology and Galois extensions
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.