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Cohomology for Bicomodules. Separable and Maschke functors

Published online by Cambridge University Press:  30 November 2007

L. El Kaoutit  and
J. Vercruysse
L. El Kaoutit
Affiliation:
Departamento de Álgebra, Facultad de Educación y Humanidades de Ceuta, Universidad de Granada, El Greco N. 10. E-51002 Ceuta, Spain, kaoutit@ugr.es.
J. Vercruysse
Affiliation:
Department of Mathematics, Faculty of Engineering, Vrije Universiteit Brussel (VUB), B-1050 Brussels, Belgium, jvercruy@vub.ac.be.
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Abstract

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].

Keywords

ComonadbicomoduleSeparable functorMaschke functor

Information

Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 1 , February 2009 , pp. 123 - 152
Copyright
Copyright © ISOPP 2009

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