Sketches and Classifying Logoi
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910367176720384 |
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| author | Di Liberti, Ivan Lobbia, Gabriele |
| author_facet | Di Liberti, Ivan Lobbia, Gabriele |
| contents | Inspired by the theory of classifying topoi for geometric theories, we define rounded sketches and logoi and provide the notion of classifying logos for a rounded sketch. Rounded sketches can be used to axiomatise all the known fragments of infinitary first order logic in $\mathbf{L}_{\infty,\infty}$, in a spectrum ranging from weaker than finitary algebraic to stronger than $λ$-geometric for $λ$ a regular cardinal. We show that every rounded sketch has an associated classifying logos, having similar properties to the classifying topos of a geometric theory. This amounts to a Diaconescu-type result for rounded sketches and (Morita small) logoi, which generalises the one for classifying topoi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sketches and Classifying Logoi Di Liberti, Ivan Lobbia, Gabriele Category Theory Logic 18A15, 03C75, 18C10, 18B25, 18C30, 18C10 Inspired by the theory of classifying topoi for geometric theories, we define rounded sketches and logoi and provide the notion of classifying logos for a rounded sketch. Rounded sketches can be used to axiomatise all the known fragments of infinitary first order logic in $\mathbf{L}_{\infty,\infty}$, in a spectrum ranging from weaker than finitary algebraic to stronger than $λ$-geometric for $λ$ a regular cardinal. We show that every rounded sketch has an associated classifying logos, having similar properties to the classifying topos of a geometric theory. This amounts to a Diaconescu-type result for rounded sketches and (Morita small) logoi, which generalises the one for classifying topoi. |
| title | Sketches and Classifying Logoi |
| topic | Category Theory Logic 18A15, 03C75, 18C10, 18B25, 18C30, 18C10 |
| url | https://arxiv.org/abs/2403.09264 |