(Pointed) Univalence in Universe Category Models of Type Theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918255027814400 |
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| author | Kapulkin, Chris Li, Yufeng |
| author_facet | Kapulkin, Chris Li, Yufeng |
| contents | We provide a formulation of the univalence axiom in a universe category model of dependent type theory that is convenient to verify in homotopy-theoretic settings. We further develop a strengthening of the univalence axiom, called pointed univalence, that is both computationally desirable and semantically natural, and verify its closure under Artin-Wraith gluing and formation of inverse diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | (Pointed) Univalence in Universe Category Models of Type Theory Kapulkin, Chris Li, Yufeng Logic in Computer Science Category Theory Logic We provide a formulation of the univalence axiom in a universe category model of dependent type theory that is convenient to verify in homotopy-theoretic settings. We further develop a strengthening of the univalence axiom, called pointed univalence, that is both computationally desirable and semantically natural, and verify its closure under Artin-Wraith gluing and formation of inverse diagrams. |
| title | (Pointed) Univalence in Universe Category Models of Type Theory |
| topic | Logic in Computer Science Category Theory Logic |
| url | https://arxiv.org/abs/2512.16697 |