Homology, Homotopy and Applications

Volume 5 (2003)

Number 1

(Co)homology of crossed modules with coefficients in a $\pi_1$-module

Pages: 261 – 296

DOI: http://dx.doi.org/10.4310/HHA.2003.v5.n1.a12

Author

Simona Paoli (Department of Mathematics, University of Warwick, Coventry, United Kingdom)

Abstract

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.

Keywords

crossed module, cotriple (co)homology, classifying space

2010 Mathematics Subject Classification

Primary 18G50. Secondary 18G30.

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