An Algebraic Abstraction of the Localic Sheafification via the Tripos-to-Topos Construction
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917070658076672 |
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| author | Maietti, Maria Emilia Trotta, Davide |
| author_facet | Maietti, Maria Emilia Trotta, Davide |
| contents | Localic and realizability toposes are two central classes of toposes in categorical logic, both arising through the Hyland-Johnstone-Pitts tripos-to-topos construction. We investigate their shared geometric features by providing an algebraic abstraction of the notions of localic presheaves, sheafification and their connection to supercompactification of a locale via an instance of the Comparison Lemma. This can be applied to a broad class of toposes obtained to the tripos-to-topos constructions, including all those generated from a tripos based on the classical category of ZFC-sets. These results provide a unified geometric framework for understanding localic and realizability toposes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06945 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Algebraic Abstraction of the Localic Sheafification via the Tripos-to-Topos Construction Maietti, Maria Emilia Trotta, Davide Category Theory Logic 18C10, 18C50, 03G30, 18D30 Localic and realizability toposes are two central classes of toposes in categorical logic, both arising through the Hyland-Johnstone-Pitts tripos-to-topos construction. We investigate their shared geometric features by providing an algebraic abstraction of the notions of localic presheaves, sheafification and their connection to supercompactification of a locale via an instance of the Comparison Lemma. This can be applied to a broad class of toposes obtained to the tripos-to-topos constructions, including all those generated from a tripos based on the classical category of ZFC-sets. These results provide a unified geometric framework for understanding localic and realizability toposes. |
| title | An Algebraic Abstraction of the Localic Sheafification via the Tripos-to-Topos Construction |
| topic | Category Theory Logic 18C10, 18C50, 03G30, 18D30 |
| url | https://arxiv.org/abs/2511.06945 |