Dendroidal Segal spaces and infinity-operads
Abstract
We introduce the dendroidal analogs of the notions of complete Segal space and of Segal category, and construct two appropriate model categories for which each of these notions corresponds to the property of being fibrant. We prove that these two model categories are Quillen equivalent to each other, and to the monoidal model category for infinity-operads which we constructed in an earlier paper. By slicing over the monoidal unit objects in these model categories, we derive as immediate corollaries the known comparison results between Joyal's quasi-categories, Rezk's complete Segal spaces, and Segal categories.
Keywords
Cite
@article{arxiv.1010.4956,
title = {Dendroidal Segal spaces and infinity-operads},
author = {Denis-Charles Cisinski and Ieke Moerdijk},
journal= {arXiv preprint arXiv:1010.4956},
year = {2013}
}
Comments
We replaced a wrong technical lemma by a correct proposition at the begining of Section 8. This does not affect the main results of this article (in particular, the end of Section 8 is unchanged). To appear in J. Topol