Modular operads and the nerve theorem

@article{Hackney2020ModularOA,
  title={Modular operads and the nerve theorem},
  author={Philip Hackney and Marcy Robertson and Donald Yau},
  journal={Advances in Mathematics},
  year={2020},
  volume={370},
  pages={107206}
}
Abstract We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular operads. The associated singular functor from modular operads to presheaves is fully faithful, and its essential image can be classified by a Segal condition. This theorem can be used to recover a related statement, due to Andre Joyal and Joachim Kock, concerning a larger category of undirected graphs whose functor to modular operads is not just faithful but… Expand
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