English

On the normality of Higgins commutators

Category Theory 2015-02-19 v2

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.

Keywords

Cite

@article{arxiv.1312.5474,
  title  = {On the normality of Higgins commutators},
  author = {Alan S. Cigoli and James R. A. Gray and Tim Van der Linden},
  journal= {arXiv preprint arXiv:1312.5474},
  year   = {2015}
}

Comments

15 pages; final published version