Cohomology of Modules Over H-categories and Co-H-categories

摘要

Let H be a Hopf algebra. We consider H-equivariant modules over a Hopf module category C as modules over the smash extension C#H. We construct Grothendieck spectral sequences for the cohomologies as well as the H-locally finite cohomologies of these objects. We also introduce relative (D,H)-Hopf modules over a Hopf comodule category D. These generalize relative (A, H)-Hopf modules over an H-comodule algebra A. We construct Grothendieck spectral sequences for their cohomologies by using their rational Hom objects and higher derived functors of coinvariants.