Higher quasi-categories vs higher Rezk spaces
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 \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.
Keywords
Cite
@article{arxiv.1206.4354,
title = {Higher quasi-categories vs higher Rezk spaces},
author = {Dimitri Ara},
journal= {arXiv preprint arXiv:1206.4354},
year = {2020}
}
Comments
44 pages, v2: terminology changed (see Remark 5.27), Corollary 7.5 added, appendix A added, references added, v3: reorganization of Sections 5 and 6, more informal comments, new section characterizing strict n-categories whose nerve is an n-quasi-category, numbering has changed