Homology, Homotopy and Applications
Volume 18 (2016)
Monoids and pointed $S$-protomodular categories
Pages: 151 – 172
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.
fibration of points, Mal’tsev and protomodular categories, monoid with operations, Schreier split epimorphism, pointed $S$-protomodular category
2010 Mathematics Subject Classification
03C05, 08C05, 18D35, 18G50