SEMILATTICES WITH A CONGRUENCE

A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition.We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence, hence equivalent to the category of semilattice epimorphisms.Guided by the above example, we recall an "internal" characterization of surjective homomorphisms between general relational systems.