On the cohomology of comodules over smash coproducts

Abstract

We consider the category of comodules over a smash coproduct coalgebra C H. We show that there is a Grothendieck spectral sequence connecting the derived functors of the Hom functors coming from C H-colinear, $H$-colinear and rational $C$-colinear morphisms. We give several applications and connect our results to existing spectral sequences in the literature.