(Co)homology of crossed modules with coefficients in a $π_1$-module

Details (Co)homology of crossed modules with coefficients in a $π_1$-module (Co)homology of crossed modules with coefficients in a $π_1$-module

2003-06-04

arxiv.org/abs/math/0306079v2

Mathematics

Algebraic Topology

32 pages, LaTeX2e, Paul Taylor's diagram package; added reference. Accepted for publication by Homology, Homotopy and Applicat

Scientific paper

We define a cotriple (co)homology of crossed modules with coefficients in a $\pi_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with the (co)homology of the classifying space of a crossed module and with the cohomology of groups with operators. An example and an application are given.

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