|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Rigidification of
cubical quasicategories
Pierre-Louis Curien, Muriel Livernet and Gabriel Saadia |
|
Algebraic & Geometric Topology 24 (2024) 2851–2888
|
 |
Abstract |
|
We construct a cubical analogue of the rigidification functor from quasicategories to simplicial categories present in the work of Joyal and Lurie. We define a functor from the category of cubical sets of Doherty, Kapulkin, Lindsey, and Sattler to the category of (small) simplicial categories. We show that this rigidification functor establishes a Quillen equivalence between the Joyal model structure on (as it is called by the four authors) and Bergner’s model structure on . We follow the approach to rigidification of Dugger and Spivak, adapting their framework of necklaces to the cubical setting. |
Keywords
Quillen model category structures, $\infty$–categories,
cubical sets, posets, weak Bruhat order on the symmetric
group
|
Mathematical Subject Classification
Primary: 18N60
Secondary: 06A07, 20B30
|
References |
Publication
Received: 26 January 2023
Revised: 12 June 2023
Accepted: 19 July 2023
Published: 19 August 2024
|
Authors |
| Pierre-Louis Curien | |
| CNRS IRIF Université Paris Cité Paris France |
|
| Muriel Livernet | |
| Université Paris Cité Institut de Mathématiques de Jussieu–Paris Rive Gauche CNRS Sorbonne Université DMA ENS-PSL Paris France |
|
| Gabriel Saadia | |
| Department of Mathematics Stockholm University Stockholm Sweden |
|
| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
