Semilattices with a congruence
arXiv:2407.08446
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 recall an ``internal'' characterization of surjective homomorphisms between general relational systems.
v2, fixed a few details; added some references to related works