Nelson Martins-Ferreira: Weakly Mal'tsev categories and strong relations

We 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 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 prove a more general result which includes, as another particular instance, a similar well known characterization of Mal'tsev categories.