Geodesic
Monoids and pointed $S$-protomodular categories
Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 151-172.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2016.v18.n1.a9
Classification : 03C05, 08C05, 18D35, 18G50
Keywords: fibration of points, Mal’tsev and protomodular categories, monoid with operations, Schreier split epimorphism, pointed $S$-protomodular category 
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     title = {Monoids and pointed $S$-protomodular categories},
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Dominique Bourn; Nelson Martins-Ferreira; Andrea Montoli; Manuela Sobral. Monoids and pointed $S$-protomodular categories. Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 151-172. doi : 10.4310/HHA.2016.v18.n1.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a9/

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