Rigidification of cubical quasi-categories - Département des mathématiques et applications de l'ENS PARIS Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Rigidification of cubical quasi-categories

Résumé

We construct a cubical analogue of the rigidification functor from quasi-categories 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-Sattler to the category of (small) simplicial categories. We show that this rigidification functor establishes a Quillen equivalence between the Joyal model structure on cubical sets (as it is called by the four authors) and Bergner's model structure on simplicial categories. We follow the approach to rigidification of Dugger and Spivak, adapting their framework of necklaces to the cubical setting.

Dates et versions

hal-03958333 , version 1 (26-01-2023)

Identifiants

Citer

Pierre-Louis Curien, Muriel Livernet, Gabriel Saadia. Rigidification of cubical quasi-categories. 2022. ⟨hal-03958333⟩
10 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More