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Cohomology for bicomodules. Separable and Maschke functors

L. El Kaoutit·J. Vercruysse
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Abstract

We introduce the category of bicomodules for a comonad in 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 [11], and the characterization of coseparable coalgebras coextensions stated in [16].

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L. El Kaoutit, J. Vercruysse. 2006-08-08. Cohomology for bicomodules. Separable and Maschke functors. https://arxiv.org/abs/math/0608195

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