Hochschild-Mitchell cohomology and Galois extensions

الأصل · EN

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.