Higher Structures, Vol. 7, No. 1, pp. 74-165, 2023

Synthetic fibered (∞,1)-category theory

Jonathan Weinberger, Ulrik Buchholtz

Received May 4th 2021. Published online May 21st 2023.

Abstract:  We study cocartesian fibrations in the setting of the synthetic (∞,1)-category theory developed in simplicial type theory introduced by Riehl and Shulman. Our development culminates in a Yoneda Lemma for cocartesian fibrations.
Keywords:  homotopy type theory; simplicial type theory; (∞; 1)-categories; Segal spaces; Rezk spaces; cartesian fibrations
Classification MSC:  03B38, 18N60, 18N45, 18D30, 18N55, 55U35, 18N50, 18D40, 18D70

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