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A
cubical model for $(\infty, n)$-categories
Tim Campion, Krzysztof Kapulkin and Yuki Maehara |
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Geometry & Topology 29 (2025) 1115–1170
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Abstract |
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We propose a new model for the theory of -categories (including the case ) in the category of marked cubical sets with connections, similar in flavor to complicial sets of Verity. The model structure characterizing our model is shown to be monoidal with respect to suitably defined (lax and pseudo) Gray tensor products; in particular, these tensor products are both associative and biclosed. Furthermore, we show that the triangulation functor to precomplicial sets is a left Quillen functor and is strong monoidal with respect to both Gray tensor products. |
Keywords
cubical set, $(\infty,n)$-category, Gray tensor product,
model category, triangulation
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Mathematical Subject Classification
Primary: 18N65
Secondary: 18N40, 55U35, 55U40
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References |
Publication
Received: 1 June 2020
Revised: 28 February 2024
Accepted: 31 May 2024
Published: 31 May 2025
Proposed: Mark Behrens
Seconded: Leonid Polterovich, Ulrike Tillmann
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Authors |
| Tim Campion | |
| Department of Mathematics Johns Hopkins University Baltimore, MD United States |
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| Krzysztof Kapulkin | |
| Department of Mathematics University of Western Ontario London, ON Canada |
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| Yuki Maehara | |
| Research Institute for Mathematical
Sciences Kyoto University Kyoto Japan |
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| © 2025 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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