Semilattices with a congruence
Rings and Algebras
2025-07-14 v2
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.
Cite
@article{arxiv.2407.08446,
title = {Semilattices with a congruence},
author = {Paolo Lipparini},
journal= {arXiv preprint arXiv:2407.08446},
year = {2025}
}
Comments
v2, fixed a few details; added some references to related works