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Higher Quasi-Categories vs Higher Rezk Spaces

Published online by Cambridge University Press:  22 May 2015

Dimitri Ara
Dimitri Ara*
Affiliation:
Institut de Mathématiques de Jussieu, Université Paris Diderot – Paris 7, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France, E-mail address: ara@math.jussieu.fr, URL: http://people.math.jussieu.fr/~ara/
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Abstract

We introduce a notion of n-quasi-categories as fibrant objects of a model category structure on presheaves on Joyal's n-cell category Θn. Our definition comes from an idea of Cisinski and Joyal. However, we show that this idea has to be slightly modified to get a reasonable notion. We construct two Quillen equivalences between the model category of n-quasi-categories and the model category of Rezk Θn-spaces, showing that n-quasi-categories are a model for (∞, n)-categories. For n = 1, we recover the two Quillen equivalences defined by Joyal and Tierney between quasi-categories and complete Segal spaces.

Keywords

18D0518D2018E3518G3018G5555U1055U3555U40∞, n-categoriesquasi-categoriesn-quasi-categoriesSegal spacesΘn-spacesA-localizers
Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 3 , December 2014 , pp. 701 - 749
Copyright
Copyright © ISOPP 2014 

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