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An explicit comparison between $2$–complicial sets and $\Theta_2$–spaces

Julia E Bergner, Viktoriya Ozornova and Martina Rovelli

Algebraic & Geometric Topology 24 (2024) 3827–3873
Abstract

We produce a direct Quillen equivalence between two models of (,2)–categories: the complete Segal Θ2–spaces due to Rezk and the 2–complicial sets due to Verity.

Keywords
$(\infty,2)$–categories, $2$–categories, complicial sets, complete Segal $\Theta_2$–spaces
Mathematical Subject Classification
Primary: 18N10, 18N65, 55U35
Secondary: 18N50, 55U10
References
Publication
Received: 26 September 2022
Revised: 2 August 2023
Accepted: 17 September 2023
Published: 9 December 2024
Authors
Julia E Bergner
Department of Mathematics
University of Virginia
Charlottesville, VA
United States
Viktoriya Ozornova
Max Planck Institute for Mathematics
Bonn
Germany
Martina Rovelli
Department of Mathematics and Statistics
University of Massachusetts at Amherst
Amherst, MA
United States

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