English

Normalities and Commutators

Category Theory 2010-02-09 v1

Abstract

We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any semi-abelian category the following well-known characterization of normal subgroups: a subobject KK is normal in AA if, and only if, [A,K]K[A,K]\leq K.

Keywords

Cite

@article{arxiv.1002.1372,
  title  = {Normalities and Commutators},
  author = {Sandra Mantovani and Giuseppe Metere},
  journal= {arXiv preprint arXiv:1002.1372},
  year   = {2010}
}
R2 v1 2026-06-21T14:44:07.243Z