The representing localic groupoid for a geometric theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912001269170176 |
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| author | Manuell, Graham Wrigley, Joshua L. |
| author_facet | Manuell, Graham Wrigley, Joshua L. |
| contents | We give an expository, and hopefully approachable, account of the Joyal-Tierney result that every topos can be represented as a topos of sheaves on a localic groupoid. We give an explicit presentation of a representing localic groupoid for the classifying topos of a given geometric theory and discuss links with the topological groupoids of Forssell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15209 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The representing localic groupoid for a geometric theory Manuell, Graham Wrigley, Joshua L. Category Theory Algebraic Geometry Logic 18F10, 22A22, 03G30, 06D22, 18B25 We give an expository, and hopefully approachable, account of the Joyal-Tierney result that every topos can be represented as a topos of sheaves on a localic groupoid. We give an explicit presentation of a representing localic groupoid for the classifying topos of a given geometric theory and discuss links with the topological groupoids of Forssell. |
| title | The representing localic groupoid for a geometric theory |
| topic | Category Theory Algebraic Geometry Logic 18F10, 22A22, 03G30, 06D22, 18B25 |
| url | https://arxiv.org/abs/2305.15209 |