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Main Authors:	Curien, Pierre-Louis, Livernet, Muriel, Saadia, Gabriel
Format:	Preprint
Published:	2022
Subjects:	Algebraic Topology Category Theory 18Nxx, 18N60, 06A07, 20B30
Online Access:	https://arxiv.org/abs/2211.13679
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author	Curien, Pierre-Louis Livernet, Muriel Saadia, Gabriel
author_facet	Curien, Pierre-Louis Livernet, Muriel Saadia, Gabriel
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2211_13679
institution	arXiv
publishDate	2022
record_format	arxiv
spellingShingle	Rigidification of cubical quasi-categories Curien, Pierre-Louis Livernet, Muriel Saadia, Gabriel Algebraic Topology Category Theory 18Nxx, 18N60, 06A07, 20B30 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.
title	Rigidification of cubical quasi-categories
topic	Algebraic Topology Category Theory 18Nxx, 18N60, 06A07, 20B30
url	https://arxiv.org/abs/2211.13679

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