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

• Autores: Krzysztof Kapulkin, Karol Szumiło
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 2, 2019
• Idioma: inglés
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• Resumen

  • 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.