Interpreting type theory in a quasicategory: a Yoneda approach

El Mehdi Cherradi

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arXiv · 2207.01967

Interpreting type theory in a quasicategory: a Yoneda approach

El Mehdi Cherradi

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Abstract

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-L\"of type theory with $\Pi$-types. This mapping procedure restricts so that elementary higher topoi yield models of homotopy type theory.

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BibTeX RIS

El Mehdi Cherradi. 2022-07-05. Interpreting type theory in a quasicategory: a Yoneda approach. https://arxiv.org/abs/2207.01967

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