  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.

Algebraic Topology;Category Theory