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Higher Quasi-Categories vs Higher Rezk Spaces
Dimitri Ara
Journal:

Journal of K-Theory / Volume 14 / Issue 3 / December 2014

Published online by Cambridge University Press:

22 May 2015, pp. 701-749

Print publication:

December 2014
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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 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.