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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.02063 |
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| _version_ | 1866916504292818944 |
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| author | Gimenez, B. Pelaitay, G. Zuluaga, W. |
| author_facet | Gimenez, B. Pelaitay, G. Zuluaga, W. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Stone-type duality for semilattices with adjunctions Gimenez, B. Pelaitay, G. Zuluaga, W. Logic 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. |
| title | A Stone-type duality for semilattices with adjunctions |
| topic | Logic |
| url | https://arxiv.org/abs/2412.02063 |