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 (Pré-Publicações DMUC 16–21, 1–41 2016) which characterises groups amongst monoids as the protomodular objects.
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Supported by Ministerio de Economí a y Competitividad (Spain), grants MTM2013-43687-P and MTM2016-79661-P (European FEDER support included), by Xunta de Galicia, grant GRC2013-045 (European FEDER support included), and by an FPU scholarship of the Ministerio de Educación, Cultura y Deporte (Spain).
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García-Martínez, X. A New Characterisation of Groups Amongst Monoids. Appl Categor Struct 25, 659–661 (2017). https://doi.org/10.1007/s10485-016-9471-x
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DOI: https://doi.org/10.1007/s10485-016-9471-x