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.

Keywords: Specialization semilattice; specialization poset; epimorphism; semilattice with a congruence; compatible preorder; arrow category of epimorphisms.

MSC: 06A12, 54A05, 18A25

DOI: 10.57016/MV-XWSF5683

Pages:  1--9