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Discreteness and
completeness for $\Theta_n$-models of
$(\infty,n)$-categories
Julia E. Bergner |
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Vol. 6 (2024), No. 1, 49–96
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Abstract |
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We establish cartesian model structures for variants of -spaces in which we replace some or all of the completeness conditions by discreteness conditions. We prove that they are all equivalent to each other and to the -space model, and we give a criterion for which combinations of discreteness and completeness give nonoverlapping models. These models can be thought of as generalizations of Segal categories in the framework of -diagrams. In the process, we give a characterization of the Dwyer–Kan equivalences in the -space model, generalizing the one given by Rezk for complete Segal spaces. A correction was submitted on 11 Dec 2024 and posted online on 14 Dec 2024. |
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Keywords
$(\infty,n)$-category, model category, $\Theta_n$-space,
Segal category, Dwyer–Kan equivalence
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Mathematical Subject Classification
Primary: 18N65, 18N50, 18N40
Secondary: 55U35, 55U40, 18D15, 18D20, 18G30, 18G55
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Milestones
Received: 21 October 2022
Revised: 12 May 2023
Accepted: 29 May 2023
Published: 20 January 2024
Correction posted: 12 Dec 2024
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Authors |
| Julia E. Bergner | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
