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separable functor

Journal of K-Theory (1)

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Cohomology for Bicomodules. Separable and Maschke functors
L. El Kaoutit, J. Vercruysse
Journal:

Journal of K-Theory / Volume 3 / Issue 1 / February 2009

Published online by Cambridge University Press:

30 November 2007, pp. 123-152

Print publication:

February 2009
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We introduce the category of bicomodules for a comonad on a Grothendieck category whose underlying functor is right exact and preserves direct sums. 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].