Monoids and pointed S-protomodular categories

Bourn, Dominique; Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela

http://hdl.handle.net/10400.8/13632

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Authors

Bourn, Dominique

Martins-Ferreira, Nelson

Montoli, Andrea

Sobral, Manuela

Abstract(s)

We 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.