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An explicit comparison
between $2$–complicial sets and $\Theta_2$–spaces
Julia E Bergner, Viktoriya Ozornova and Martina Rovelli |
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Algebraic & Geometric Topology 24 (2024) 3827–3873
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Abstract |
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We produce a direct Quillen equivalence between two models of –categories: the complete Segal –spaces due to Rezk and the –complicial sets due to Verity. |
Keywords
$(\infty,2)$–categories, $2$–categories, complicial sets,
complete Segal $\Theta_2$–spaces
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Mathematical Subject Classification
Primary: 18N10, 18N65, 55U35
Secondary: 18N50, 55U10
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References |
Publication
Received: 26 September 2022
Revised: 2 August 2023
Accepted: 17 September 2023
Published: 9 December 2024
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Authors |
| Julia E Bergner | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
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| Viktoriya Ozornova | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| Martina Rovelli | |
| Department of Mathematics and
Statistics University of Massachusetts at Amherst Amherst, MA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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