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Internal Languages of Finitely Complete $(\infty, 1)$-categories
Published 27 Sep 2017 in math.CT, math.AT, and math.LO | (1709.09519v2)
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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