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arXiv · 1312.5474

On the normality of Higgins commutators

Alan S. Cigoli·James R. A. Gray·Tim Van der Linden
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Abstract

In a semi-abelian context, we study the condition (NH) asking that Higgins commutators of normal subobjects are normal subobjects. We provide examples of categories that do or do not satisfy this property. We focus on the relationship with the "Smith is Huq" condition (SH) and characterise those semi-abelian categories in which both (NH) and (SH) hold in terms of reflection and preservation properties of the change of base functors of the fibration of points.

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Alan S. Cigoli, James R. A. Gray, Tim Van der Linden. 2013-12-19. On the normality of Higgins commutators. https://doi.org/10.1016/j.jpaa.2014.05.025

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