English

Normalizers in the non-pointed context: a weak case of extremal decomposition

Category Theory 2021-10-28 v1

Abstract

The aim of this work is to point out a strong structural phenomenon hidden behind the existence of normalizers through the investigation of this property in the non-pointed context: given any category E, a certain property of the fibration of points: Pt(E) --> E guarentees the existence of normalizers. This property becomes a characterization of this existence when E is quasi-pointed and protomodular. This property is also showed to be equivalent to a property of the category GrdE of internal groupoids in E which is a kind of opposite, for the monomorphic internal functors, of the comprehensive factorization.

Keywords

Cite

@article{arxiv.2110.14280,
  title  = {Normalizers in the non-pointed context: a weak case of extremal decomposition},
  author = {Dominique Bourn},
  journal= {arXiv preprint arXiv:2110.14280},
  year   = {2021}
}

Comments

33 pages

R2 v1 2026-06-24T07:13:36.151Z