Janelidze, ZurabMartins-Ferreira, Nelson2025-10-292025-10-292012Janelidze, Z., & Martins-Ferreira, N. (2012). Weakly Mal’tsev categories and strong relations. Theory and Applications of Categories, 27(5), 65-79.1201-561Xhttp://hdl.handle.net/10400.8/14424We 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.engDifunctional relationFactorization systemMal'tsev categoryWeakly Mal'tsev categoryjournal article