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Bourn-normal monomorphisms in regular Mal'tsev categories
Theory and applications of categories, Tome 32 (2017), pp. 122-147
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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.

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Classification : 18D30, 18C05, 08A30
Keywords: normal monomorphism, Mal'tsev category, fibred category 
@article{TAC_2017_32_a4,
     author = {Giuseppe Metere},
     title = {Bourn-normal monomorphisms in regular {Mal'tsev} categories},
     journal = {Theory and applications of categories},
     pages = {122--147},
     year = {2017},
     volume = {32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a4/}
}
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Giuseppe Metere. Bourn-normal monomorphisms in regular Mal'tsev categories. Theory and applications of categories, Tome 32 (2017), pp. 122-147. http://geodesic.mathdoc.fr/item/TAC_2017_32_a4/