English

A new characterisation of groups amongst monoids

Category Theory 2016-06-09 v1

Abstract

We prove that a monoid MM is a group if and only if, in the category of monoids, all points over MM are strong. This sharpens and greatly simplifies a result of Montoli, Rodelo and Van der Linden which characterises groups amongst monoids as the protomodular objects.

Keywords

Cite

@article{arxiv.1606.02490,
  title  = {A new characterisation of groups amongst monoids},
  author = {Xabier García-Martínez},
  journal= {arXiv preprint arXiv:1606.02490},
  year   = {2016}
}
R2 v1 2026-06-22T14:20:23.432Z