(Co)homology of crossed modules with coefficients in a ${\pi }_1$-module

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.

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