Bourn-normal monomorphisms in regular Mal’tsev categories
- Authors: Metere, G.
- Publication year: 2017
- Type: Articolo in rivista (Articolo in rivista)
- Key words: Fibred category; Mal’tsev category; Normal monomorphism;
Normal monomorphisms in the sense of Bourn describe the equivalence classes of an internal equivalence relation. Although the definition is given in the fairly general setting of a category with finite limits, later investigations on this subject often focus on protomodular settings, where normality becomes a property. This paper clarifies the connections between internal equivalence relations and Bourn-normal monomorphisms in regular Mal’tesv categories with pushouts of split monomorphisms along arbitrary morphisms, whereas a full description is achieved for quasi-pointed regular Mal’tsev categories with pushouts of split monomorphisms along arbitrary morphisms.