English

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.

Keywords

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

R2 v1 2026-06-28T17:37:16.388Z