Resumen de Internal languages of finitely complete (\infty , 1)-categories

Krzysztof Kapulkin, Karol Szumiło

• 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-Löf Type Theory with dependent sums and intensional identity types is the internal language of (∞,1) -categories with finite limits.