Cohomology for bicomodules: Separable and Maschke functors

摘要

We introduce the category of bicomodules for a comonad on a Grothendieck category whose underlying functor is right exact and preserves direct sum. We characterize comonads with a separable forgetful functor by means of cohomology groups using cointegrations into bicomodules. We present two applications: the characterization of coseparable corings stated in [14], and the characterization of coseparable coalgebra coextensions stated in [19].