Percorrer por autor "Bourn, Dominique"
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- Monoids and pointed S-protomodular categoriesPublication . Bourn, Dominique; Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, ManuelaWe investigate the notion of pointed S-protomodular category, with respect to a suitable class S of points, and we prove that these categories satisfy, relatively to the class S, many partial aspects of the properties of Mal’tsev and protomodular categories, like the split short five lemma for S-split exact sequences, or the fact that a reflexive S-relation is transitive. The main examples of S-protomodular categories are the category of monoids and, more generally, any category of monoids with operations, where the class S is the class of Schreier points.
- Schreier split epimorphisms between monoidsPublication . Bourn, Dominique; Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, ManuelaWe 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.