Browsing by Author "Janelidze, Zurab"
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- Weakly Mal’tsev Categories and Strong RelationsPublication . Janelidze, Zurab; Martins-Ferreira, NelsonWe define a strong relation in a category 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 → X × Y . We show that a category C with pullbacks and equalizers is a weakly Mal’tsev category if and only if every reflexive strong relation in 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.