Browsing by Author "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.