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2012 Higher cohomologies of modules
María Calvo, Antonio M Cegarra, Nguyen T Quang
Algebr. Geom. Topol. 12(1): 343-413 (2012). DOI: 10.2140/agt.2012.12.343

Abstract

If is a small category, then a right –module is a contravariant functor from into abelian groups. The abelian category Mod of right –modules has enough projective and injective objects, and the groups ExtModn(B,A) provide the basic cohomology theory for –modules. We introduce, for each integer r1, an approach for a level– r cohomology theory for –modules by defining cohomology groups H[b],rn(B,A), n0, which are the focus of this article. Applications to the homotopy classification of braided and symmetric –fibred categorical groups and their homomorphisms are given.

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María Calvo. Antonio M Cegarra. Nguyen T Quang. "Higher cohomologies of modules." Algebr. Geom. Topol. 12 (1) 343 - 413, 2012. https://doi.org/10.2140/agt.2012.12.343

Information

Received: 3 February 2011; Revised: 7 November 2011; Accepted: 18 November 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1254.18006
MathSciNet: MR2916279
Digital Object Identifier: 10.2140/agt.2012.12.343

Subjects:
Primary: 18D10, 55N25
Secondary: 18D30, 55P91

Rights: Copyright © 2012 Mathematical Sciences Publishers

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