Internal Languages of Finitely Complete (infty, 1)-categories
classification
🧮 math.CT
math.ATmath.LO
keywords
categoriesinftyinternaltheoryassertingcompleteconjectureconsequence
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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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