Internal languages of locally cartesian closed $(\infty,1)$-categories
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915826425135104 |
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| author | Cherradi, El Mehdi |
| author_facet | Cherradi, El Mehdi |
| contents | We establish a DK-equivalence between the relative category of $π$-tribes and the relative category of locally cartesian closed quasicategories. From this follows one of the internal languages conjecture: Martin-Löf type theory with dependent sums, intensional identity types, and dependent products satisfying functional extensionality is the internal language of locally cartesian closed $(\infty,1)$-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Internal languages of locally cartesian closed $(\infty,1)$-categories Cherradi, El Mehdi Category Theory Algebraic Topology Logic We establish a DK-equivalence between the relative category of $π$-tribes and the relative category of locally cartesian closed quasicategories. From this follows one of the internal languages conjecture: Martin-Löf type theory with dependent sums, intensional identity types, and dependent products satisfying functional extensionality is the internal language of locally cartesian closed $(\infty,1)$-categories. |
| title | Internal languages of locally cartesian closed $(\infty,1)$-categories |
| topic | Category Theory Algebraic Topology Logic |
| url | https://arxiv.org/abs/2509.03371 |