The category of topological spaces and open maps does not have products
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914963937820672 |
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| author | Bezhanishvili, Guram Kornell, Andre |
| author_facet | Bezhanishvili, Guram Kornell, Andre |
| contents | We prove that the category of topological spaces and open maps does not have binary products, thus resolving the Esakia problem in the negative. We also prove that the categories of complete Heyting algebras and complete closure algebras do not have binary coproducts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The category of topological spaces and open maps does not have products Bezhanishvili, Guram Kornell, Andre Category Theory 18F60, 54B10, 54C10, 06D20, 06E25, 03B45 We prove that the category of topological spaces and open maps does not have binary products, thus resolving the Esakia problem in the negative. We also prove that the categories of complete Heyting algebras and complete closure algebras do not have binary coproducts. |
| title | The category of topological spaces and open maps does not have products |
| topic | Category Theory 18F60, 54B10, 54C10, 06D20, 06E25, 03B45 |
| url | https://arxiv.org/abs/2407.13951 |