Univalence in Simplicial Sets

2012/03/12 by Chris Kapulkin, Kapulkin, Chris, Peter LeFanu Lumsdaine +3 · 2 citations
Mathematics · #55U10 (Primary) 55U35 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1203.2553

openalex publication_date 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an accessible account of Voevodsky's construction of a univalent universe of Kan fibrations.

Citations

• The Simplicial Model of Univalent Foundations (after Voevodsky)

Cited by

• A self-contained, brief and complete formulation of Voevodsky's Univalence Axiom
• An introduction to univalent foundations for mathematicians

Related

• Univalent completion
• The Simplicial Model of Univalent Foundations (after Voevodsky)
• Realizability of Univalence: Modest Kan complexes
• Effective Kan fibrations in simplicial sets
• On lifting univalence to the equivariant setting