On the non-balanced property of the category of crossed modules in groups

Abstract

An algebraic category $\mathcal{C}$ is called balanced if the cotriple cohomology of any object of $\mathcal{C}$ vanishes in positive dimensions on injective coefficient modules. Important examples of balanced and of non-balanced categories occur in the literature. In this paper we prove that the category of crossed modules in groups is non-balanced.

arXiv comment12 pages, LaTeX2e, Paul Taylor's diagram package