Weakly Mal’tsev Categories and Strong Relations

Janelidze, Zurab; Martins-Ferreira, Nelson

http://hdl.handle.net/10400.8/14424

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Authors

Janelidze, Zurab

Martins-Ferreira, Nelson

Abstract(s)

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 × 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.