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arXiv · 2509.03371

Internal languages of locally cartesian closed $(\infty,1)$-categories

El Mehdi Cherradi
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Abstract

We establish a DK-equivalence between the relative category of $\pi$-tribes and the relative category of locally cartesian closed quasicategories. From this follows one of the internal languages conjecture: Martin-L\"of 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.

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El Mehdi Cherradi. 2025-09-03. Internal languages of locally cartesian closed $(\infty,1)$-categories. https://arxiv.org/abs/2509.03371

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