Symmetrization of monoïds as hypergroups

Simon Henry

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arXiv · 1309.1963

Symmetrization of monoïds as hypergroups

Simon Henry

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Abstract

We adapt the construction of the Grothendieck group associated to a commutative monoïd to handle idempotent monoïds. Our construction works for a restricted class of commutative monoïds, it agrees with the Grothendieck group construction in many cases and yields a hypergroup which solves the universal problem for morphisms to hypergroups. It gives the expected non-trivial hypergroup construction in the case of idempotent monoïds.

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Simon Henry. 2013-09-08. Symmetrization of monoïds as hypergroups. https://arxiv.org/abs/1309.1963

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