Higher cyclic operads
Abstract
We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category of trees, which carries a tight relationship to the Moerdijk-Weiss category of rooted trees . We prove a nerve theorem exhibiting colored cyclic operads as presheaves on which satisfy a Segal condition. Finally, we produce a Quillen model category whose fibrant objects satisfy a weak Segal condition, and we consider these objects as an up-to-homotopy generalization of the concept of cyclic operad.
Keywords
Cite
@article{arxiv.1611.02591,
title = {Higher cyclic operads},
author = {Philip Hackney and Marcy Robertson and Donald Yau},
journal= {arXiv preprint arXiv:1611.02591},
year = {2019}
}
Comments
This version has been accepted to AGT. Substantial updates throughout, including an alternative description (suggested by the referee) of the morphisms of $\Xi$, a new appendix, and various other improvements