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 is normal in if, and only if, .
Keywords
Cite
@article{arxiv.1002.1372,
title = {Normalities and Commutators},
author = {Sandra Mantovani and Giuseppe Metere},
journal= {arXiv preprint arXiv:1002.1372},
year = {2010}
}