Higher cyclic operads.

@article{Hackney2016HigherCO,
  title={Higher cyclic operads.},
  author={P. Hackney and M. Robertson and D. Yau},
  journal={arXiv: Algebraic Topology},
  year={2016}
}
  • P. Hackney, M. Robertson, D. Yau
  • Published 2016
  • Mathematics
  • arXiv: Algebraic Topology
  • We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category $\Xi$ of trees, which carries a tight relationship to the Moerdijk-Weiss category of rooted trees $\Omega$. We prove a nerve theorem exhibiting colored cyclic operads as presheaves on $\Xi$ which satisfy a Segal condition. Finally, we produce a Quillen model category whose fibrant objects satisfy a weak Segal condition, and we consider… CONTINUE READING
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