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arXiv · 2412.02063

A Stone-type duality for semilattices with adjunctions

B. Gimenez·G. Pelaitay·W. Zuluaga
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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.

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BibTeXRIS

B. Gimenez, G. Pelaitay, W. Zuluaga. 2024-12-03. A Stone-type duality for semilattices with adjunctions. https://arxiv.org/abs/2412.02063

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