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Pushouts of Dwyer maps
are $(\infty,1)$–categorical
Philip Hackney, Viktoriya Ozornova, Emily Riehl and Martina Rovelli |
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Algebraic & Geometric Topology 24 (2024) 2171–2183
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Abstract |
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The inclusion of –categories into –categories fails to preserve colimits in general, and pushouts in particular. We observe that if one functor in a span of categories belongs to a certain previously identified class of functors, then the –categorical pushout is preserved under this inclusion. Dwyer maps, a kind of neighborhood deformation retract of categories, were used by Thomason in the construction of his model structure on –categories. Thomason previously observed that the nerves of such pushouts have the correct weak homotopy type. We refine this result and show that the weak homotopical equivalence is a weak categorical equivalence. We also identify a more general class of functors along which –categorical pushouts are –categorical. |
Keywords
Dwyer map, nerve functor, $(\infty,1)$–category, simplicial
category, quasicategory
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Mathematical Subject Classification
Primary: 18N60, 55U35
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References |
Publication
Received: 3 June 2022
Revised: 8 March 2023
Accepted: 3 April 2023
Published: 16 July 2024
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Authors |
| Philip Hackney | |
| Department of Mathematics University of Louisiana at Lafayette Lafayette, LA United States |
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| Viktoriya Ozornova | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| Emily Riehl | |
| Department of Mathematics Johns Hopkins University Baltimore, MD United States |
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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 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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