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arXiv · 1606.02490

A new characterisation of groups amongst monoids

Xabier García-Martínez
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Abstract

We prove that a monoid $M$ is a group if and only if, in the category of monoids, all points over $M$ 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.

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Xabier García-Martínez. 2016-06-08. A new characterisation of groups amongst monoids. https://arxiv.org/abs/1606.02490

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