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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2605.21667 |
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| _version_ | 1866917518153613312 |
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| author | Zuluaga, William Gimenez, Belén |
| author_facet | Zuluaga, William Gimenez, Belén |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21667 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Multirelations to Meet-Relations: A Relational Duality for Semilattices with Adjunctions Zuluaga, William Gimenez, Belén Logic Category Theory 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. |
| title | From Multirelations to Meet-Relations: A Relational Duality for Semilattices with Adjunctions |
| topic | Logic Category Theory |
| url | https://arxiv.org/abs/2605.21667 |