Synthetic perspectives on spaces and categories
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911216969973760 |
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| author | Riehl, Emily |
| author_facet | Riehl, Emily |
| contents | Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose fundamental proof techniques from these parallel settings: describing induction principles over paths or arrows and constructions involving universes that are either univalent or directed univalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Synthetic perspectives on spaces and categories Riehl, Emily Category Theory Algebraic Topology Logic 18N60, 18N45, 55U35, 03B38 Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose fundamental proof techniques from these parallel settings: describing induction principles over paths or arrows and constructions involving universes that are either univalent or directed univalent. |
| title | Synthetic perspectives on spaces and categories |
| topic | Category Theory Algebraic Topology Logic 18N60, 18N45, 55U35, 03B38 |
| url | https://arxiv.org/abs/2510.15795 |