Synthetic fibered (∞,1)-category theory

2021/05/04 by Ulrik Buchholtz, Buchholtz, Ulrik, Jonathan Weinberger +1 · 1 citation
Mathematics · #03B38 #18D30 #18D40 #18D70 #18N45 #18N50 #18N55 #18N60 #55U35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic in Computer Science (cs.LO)

paper · pdf · doi:10.48550/arxiv.2105.01724

openalex publication_date 2021/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study cocartesian fibrations in the setting of the synthetic (∞,1)-category theory developed in the simplicial type theory introduced by Riehl and Shulman. Our development culminates in a Yoneda Lemma for cocartesian fibrations.

Citations

• The stack of higher internal categories and stacks of iterated spans
• Quasi-categories and Kan complexes

Cited by

• Yoneda Lemma for D-Simplicial Spaces

Related

• Two-sided cartesian fibrations of synthetic (∞,1)-categories
• Fibrations and Yoneda's lemma in an ∞-cosmos
• Yoneda Lemma for D-Simplicial Spaces
• Fibrations in ∞-category theory
• Formalizing the ∞-Categorical Yoneda Lemma