Internal Parameterization of Hyperconnected Quotients
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909846363701248 |
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| author | Hora, Ryuya |
| author_facet | Hora, Ryuya |
| contents | One of the most fundamental facts in topos theory is the internal parameterization of subtoposes: the bijective correspondence between subtoposes and Lawvere-Tierney topologies. In this paper, we introduce a new but elementary concept, "a local state classifier," and give an analogous internal parameterization of hyperconnected quotients (i.e., hyperconnected geometric morphisms from a topos). As a corollary, we obtain a solution to the Boolean case of the first problem of Lawvere's open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06851 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Internal Parameterization of Hyperconnected Quotients Hora, Ryuya Category Theory 18B25 One of the most fundamental facts in topos theory is the internal parameterization of subtoposes: the bijective correspondence between subtoposes and Lawvere-Tierney topologies. In this paper, we introduce a new but elementary concept, "a local state classifier," and give an analogous internal parameterization of hyperconnected quotients (i.e., hyperconnected geometric morphisms from a topos). As a corollary, we obtain a solution to the Boolean case of the first problem of Lawvere's open problems. |
| title | Internal Parameterization of Hyperconnected Quotients |
| topic | Category Theory 18B25 |
| url | https://arxiv.org/abs/2302.06851 |