From coextensive varieties to the Gaeta topos
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912730032635904 |
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| author | Zuluaga, William |
| author_facet | Zuluaga, William |
| contents | In this paper, we show that in every coextensive variety V, the assignment that maps each algebra to its set of central elements is both functorial and representable. Furthermore, we prove that the full subcategory of finitely presented algebras in V is coextensive. Finally, we establish that if V is additionally (0, 1)-dense, the Gaeta topos classifies central-free V-models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_00135 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | From coextensive varieties to the Gaeta topos Zuluaga, William Category Theory Logic 18C10, 18D35, 18F10, 18B25 In this paper, we show that in every coextensive variety V, the assignment that maps each algebra to its set of central elements is both functorial and representable. Furthermore, we prove that the full subcategory of finitely presented algebras in V is coextensive. Finally, we establish that if V is additionally (0, 1)-dense, the Gaeta topos classifies central-free V-models. |
| title | From coextensive varieties to the Gaeta topos |
| topic | Category Theory Logic 18C10, 18D35, 18F10, 18B25 |
| url | https://arxiv.org/abs/2202.00135 |