A graphical category for higher modular operads

@article{Hackney2019AGC,
  title={A graphical category for higher modular operads},
  author={Philip Hackney and Marcy Robertson and Donald Yau},
  journal={arXiv: Algebraic Topology},
  year={2019}
}
We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Quillen model structure on the collection of simplicial presheaves for a certain category of undirected graphs. This new category of undirected graphs, denoted $\mathbf{U}$, plays a similar role for modular operads that the dendroidal category $\Omega$ plays for operads. We carefully study properties of $\mathbf{U… Expand

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