Geodesic
Mal'tsev objects, $R_1$-spaces and ultrametric spaces
Theory and applications of categories, Tome 32 (2017), pp. 1485-1500

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

In this paper we introduce a notion of Mal'tsev object, and the dual notion of co-Mal'tsev object, in a general category. In particular, a category C is a Mal'tsev category if and only if every object in C is a Mal'tsev object. We show that for a well-powered regular category C which admits coproducts, the full subcategory of Mal'tsev objects is coreflective in C. We show that the co-Mal'tsev objects in the category of topological spaces and continuous maps are precisely the $R_1$-spaces, and that the co-Mal'tsev objects in the category of metric spaces and short maps are precisely the ultrametric spaces.

Publié le :
Classification : 18A05, 18A32, 18B30, 54D10, 54E35
Keywords: Mal'tsev object, Mal'tsev category, $R_1$-space, ultrametric space 
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     author = {Thomas Weighill},
     title = {Mal'tsev objects, $R_1$-spaces and ultrametric spaces},
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     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a41/}
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Thomas Weighill. Mal'tsev objects, $R_1$-spaces and ultrametric spaces. Theory and applications of categories, Tome 32 (2017), pp. 1485-1500. http://geodesic.mathdoc.fr/item/TAC_2017_32_a41/