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arXiv · 1709.09519

Internal Languages of Finitely Complete $(\infty, 1)$-categories

Chris Kapulkin·Karol Szumiło
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Abstract

We prove that the homotopy theory of Joyal's tribes is equivalent to that of fibration categories. As a consequence, we deduce a variant of the conjecture asserting that Martin-L\"of Type Theory with dependent sums and intensional identity types is the internal language of $(\infty, 1)$-categories with finite limits.

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Chris Kapulkin, Karol Szumiło. 2017-09-27. Internal Languages of Finitely Complete $(\infty, 1)$-categories. https://arxiv.org/abs/1709.09519

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