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

Simona Paoli
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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.

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Simona Paoli. 2003-09-24. On the non-balanced property of the category of crossed modules in groups. https://arxiv.org/abs/math/0309400

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