Higher quasi-categories vs higher Rezk spaces

By D. Ara. 2012

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We introduce a notion of n-quasi-categories as fibrant objects of a model category structure on presheaves on Joyal's n-cell category \Theta_n. 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 \Theta_n-spaces showing that n-quasi-categories are a model for (\infty, n)-categories. For n = 1, we recover the two Quillen equivalences defined by Joyal and Tierney between quasi-categories and complete Segal spaces.

Subfields: Artificial Intelligence, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/903911f5d876676a2ca444f1cc1ee67a68580d24