Geodesic
Weakly Mal'tsev categories and strong relations
Theory and applications of categories, CT2011, Tome 27 (2012), pp. 65-79

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We define a strong relation in a category $\mathbb{C}$ to be a span which is ``orthogonal'' to the class of jointly epimorphic pairs of morphisms. Under the presence of finite limits, a strong relation is simply a strong monomorphism $R\rightarrow X\times Y$. We show that a category $\mathbb{C}$ with pullbacks and equalizers is a weakly Mal'tsev category if and only if every reflexive strong relation in $\mathbb{C}$ is an equivalence relation. In fact, we obtain a more general result which includes, as its another particular instance, a similar well-known characterization of Mal'tsev categories.

Publié le :
Classification : 18C99, 18A20
Keywords: weakly Mal'tsev category, Mal'tsev category, difunctional relation, factorization system 
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     author = {Zurab Janelidze and Nelson Martins-Ferreira},
     title = {Weakly {Mal'tsev} categories and strong relations},
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     publisher = {mathdoc},
     volume = {27},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_27_a4/}
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Zurab Janelidze; Nelson Martins-Ferreira. Weakly Mal'tsev categories and strong relations. Theory and applications of categories, CT2011, Tome 27 (2012), pp. 65-79. http://geodesic.mathdoc.fr/item/TAC_2012_27_a4/