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Higher cohomologies of
modules
María Calvo, Antonio M Cegarra and Nguyen T Quang |
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Algebraic & Geometric Topology 12 (2012) 343–413
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Abstract |
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If is a small category, then a right –module is a contravariant functor from into abelian groups. The abelian category of right –modules has enough projective and injective objects, and the groups provide the basic cohomology theory for –modules. We introduce, for each integer , an approach for a level– cohomology theory for –modules by defining cohomology groups , , which are the focus of this article. Applications to the homotopy classification of braided and symmetric –fibred categorical groups and their homomorphisms are given. |
Keywords
module, simplicial set, Eilenberg–Mac Lane complex,
homotopy colimit, cohomology, fibred braided monoidal
category
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Mathematical Subject Classification 2010
Primary: 18D10, 55N25
Secondary: 55P91, 18D30
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References |
Publication
Received: 3 February 2011
Revised: 7 November 2011
Accepted: 18 November 2011
Published: 14 March 2012
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Authors |
| María Calvo | |
| Department of Algebra Faculty of Sciences University of Granada Campus Fuentenueva 18071 Granada Spain |
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| Antonio M Cegarra | |
| Department of Algebra University of Granada Campus Fuentenueva, Faculty of Sciences 18071 Granada Spain |
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| Nguyen T Quang | |
| Department of Mathematics Hanoi National University of Education Xuan Thuy Street, Cau Giay district Hanoi 136 Vietnam |
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