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.
On the normality of Higgins commutators / A.S. Cigoli, J.R.A. Gray, T. Van der Linden. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 219:4(2015 Apr), pp. 897-912. [10.1016/j.jpaa.2014.05.025]
On the normality of Higgins commutators
A.S. CigoliPrimo
;
2015
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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