Dendroidal sets as models for homotopy operads
Abstract
The homotopy theory of infinity-operads is defined by extending Joyal's homotopy theory of infinity-categories to the category of dendroidal sets. We prove that the category of dendroidal sets is endowed with a model category structure whose fibrant objects are the infinity-operads (i.e. dendroidal inner Kan complexes). This extends the theory of infinity-categories in the sense that the Joyal model category structure on simplicial sets whose fibrant objects are the infinity-categories is recovered from the model category structure on dendroidal sets by simply slicing over the point.
Cite
@article{arxiv.0902.1954,
title = {Dendroidal sets as models for homotopy operads},
author = {Denis-Charles Cisinski and Ieke Moerdijk},
journal= {arXiv preprint arXiv:0902.1954},
year = {2014}
}
Comments
This is essentially the published version, except that we added an erratum at the end of the paper concerning the behaviour of cofibrations with respect to the tensor product of dendroidal sets