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

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

2003-09-24

arxiv.org/abs/math/0309400v1

Mathematics

Algebraic Topology

12 pages, LaTeX2e, Paul Taylor's diagram package

Scientific paper

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.

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