Relative elegance and cartesian cubes with one connection

2022/11/27 by Evan Cavallo, Cavallo, Evan, Christian Sattler +1 · 1 citation
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2211.14801

Abstract

We establish a Quillen equivalence between the Kan-Quillen model structure and a model structure, derived from a cubical model of homotopy type theory, on the category of cartesian cubical sets with one connection. We thereby identify a second model structure which both constructively models homotopy type theory and presents infinity-groupoids, the first example being the equivariant cartesian model of Awodey-Cavallo-Coquand-Riehl-Sattler.

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• Cartesian cubical model categories
• The equivariant model structure on cartesian cubical sets
• Cubical models of (∞, 1)-categories
• Algebraic models of homotopy types and the homotopy hypothesis
• Quillen model structures on the category of graphs