Duality theory for categorical theories
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916035348660224 |
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| author | Ye, Lingyuan |
| author_facet | Ye, Lingyuan |
| contents | We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids. We also study the geometry of profinite monoids via the classifying topos construction, and show it identifies them as a full sub-2-category of the 2-category of topoi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22071 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Duality theory for categorical theories Ye, Lingyuan Category Theory Logic 03C35, 03G30, We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids. We also study the geometry of profinite monoids via the classifying topos construction, and show it identifies them as a full sub-2-category of the 2-category of topoi. |
| title | Duality theory for categorical theories |
| topic | Category Theory Logic 03C35, 03G30, |
| url | https://arxiv.org/abs/2605.22071 |