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Semilattices with a congruence (2407.08446v1)
Published 11 Jul 2024 in math.RA
Abstract: 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 hint to an ``internal'' characterization of surjective homomorphisms between general relational systems.