A new characterisation of groups amongst monoids
classification
🧮 math.CT
keywords
monoidsamongstgroupscategorycharacterisationcharacterisesgreatlygroup
read the original 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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