From Multirelations to Meet-Relations: A Relational Duality for Semilattices with Adjunctions
Logic
2026-05-22 v1 Category Theory
Abstract
We develop a relational duality for semilattices with adjunctions (SLatas) based on binary meet-relations. First, we introduce the category of MoS-spaces and establish a dual equivalence with modal semilattices. Then, by means of A-relations, we define the category RelSP and prove a dual equivalence between SLata and RelSP. To compare this framework with the multirelational semantics previously developed for SLatas, we introduce the notion of normal mS-space and show that, under this condition, the multirelational structure can be canonically recovered from a meet-relation, and conversely. As a consequence, we prove that the categories RelSP and SLataSp are isomorphic.
Keywords
Cite
@article{arxiv.2605.21667,
title = {From Multirelations to Meet-Relations: A Relational Duality for Semilattices with Adjunctions},
author = {William Zuluaga and Belén Gimenez},
journal= {arXiv preprint arXiv:2605.21667},
year = {2026}
}