A Stone-type duality for semilattices with adjunctions
Logic
2024-12-04 v1
Abstract
This paper focuses on semilattices with adjunctions (SLatas), which are semilattices with a greatest element enriched with a pair of adjoint maps. We develop a spectral-style duality for SLatas, building on prior topological dualities for monotone semilattices. As an application of this duality, we characterize SLata congruences through an adaptation of lower-Vietoris-type families. Furthermore, we investigate tense operators on semilattices with a greatest element, deriving a duality for this case by extending the results obtained for SLatas.
Keywords
Cite
@article{arxiv.2412.02063,
title = {A Stone-type duality for semilattices with adjunctions},
author = {B. Gimenez and G. Pelaitay and W. Zuluaga},
journal= {arXiv preprint arXiv:2412.02063},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2109.01728 by other authors