When is the partial map classifier a Sierpiński cone?
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915275106942976 |
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| author | Pugh, Leoni Sterling, Jonathan |
| author_facet | Pugh, Leoni Sterling, Jonathan |
| contents | We study the relationship between partial map classifiers, Sierpiński cones, and axioms for synthetic higher categories and domains within univalent foundations. In particular, we show that synthetic $\infty$-categories are closed under partial map classifiers assuming Phoa's principle, and we isolate a new reflective subuniverse of types within which the Sierpiński cone (a lax colimit) can be computed as a partial map classifier by strengthening the Segal condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When is the partial map classifier a Sierpiński cone? Pugh, Leoni Sterling, Jonathan Logic in Computer Science Programming Languages Category Theory We study the relationship between partial map classifiers, Sierpiński cones, and axioms for synthetic higher categories and domains within univalent foundations. In particular, we show that synthetic $\infty$-categories are closed under partial map classifiers assuming Phoa's principle, and we isolate a new reflective subuniverse of types within which the Sierpiński cone (a lax colimit) can be computed as a partial map classifier by strengthening the Segal condition. |
| title | When is the partial map classifier a Sierpiński cone? |
| topic | Logic in Computer Science Programming Languages Category Theory |
| url | https://arxiv.org/abs/2504.06789 |