A new characterisation of groups amongst monoids
Category Theory
2016-06-09 v1
Abstract
We prove that a monoid is a group if and only if, in the category of monoids, all points over 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}
}