Homology, Homotopy and Applications
Volume 5 (2003)
(Co)homology of crossed modules with coefficients in a $\pi_1$-module
Pages: 261 – 296
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.
crossed module, cotriple (co)homology, classifying space
2010 Mathematics Subject Classification
Primary 18G50. Secondary 18G30.