We explore some properties of Schreier split epimorphisms between monoids, which correspond to monoid actions. In particular, we prove that the split short five lemma holds for monoids, when it is restricted to Schreier split epimorphisms, and that any Schreier reflexive relation is transitive, partially recovering in monoids a classical property of Mal'tsev varieties.
Schreier split epimorphisms between monoids / D. Bourn, N. Martins Ferreira, A. Montoli, M. Sobral. - In: SEMIGROUP FORUM. - ISSN 0037-1912. - 88:3(2014 Jun), pp. 739-752. [10.1007/s00233-014-9571-6]
Schreier split epimorphisms between monoids
A. Montoli
;
2014
Abstract
We explore some properties of Schreier split epimorphisms between monoids, which correspond to monoid actions. In particular, we prove that the split short five lemma holds for monoids, when it is restricted to Schreier split epimorphisms, and that any Schreier reflexive relation is transitive, partially recovering in monoids a classical property of Mal'tsev varieties.
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