Interpreting type theory in a quasicategory: a Yoneda approach
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912567283154944 |
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| author | Cherradi, El Mehdi |
| author_facet | Cherradi, El Mehdi |
| contents | We make use of a higher version of the Yoneda embedding to construct, from a given quasicategory, a tribe, as a subcategory of a well-behaved simplicial model category, that presents the same $(\infty,1)$-category as the former quasicategory. We then show that, when the quasicategory is locally cartesian closed, it is possible to further endow such a tribe with enough structure for it to provide a model of Martin-Löf type theory with $Π$-types. This mapping procedure restricts so that elementary higher topoi yield models of homotopy type theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01967 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Interpreting type theory in a quasicategory: a Yoneda approach Cherradi, El Mehdi Category Theory Algebraic Topology Logic We make use of a higher version of the Yoneda embedding to construct, from a given quasicategory, a tribe, as a subcategory of a well-behaved simplicial model category, that presents the same $(\infty,1)$-category as the former quasicategory. We then show that, when the quasicategory is locally cartesian closed, it is possible to further endow such a tribe with enough structure for it to provide a model of Martin-Löf type theory with $Π$-types. This mapping procedure restricts so that elementary higher topoi yield models of homotopy type theory. |
| title | Interpreting type theory in a quasicategory: a Yoneda approach |
| topic | Category Theory Algebraic Topology Logic |
| url | https://arxiv.org/abs/2207.01967 |