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arXiv · 1906.01144

Modular operads and the nerve theorem

Philip Hackney·Marcy Robertson·Donald Yau
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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 Andr\'e Joyal and Joachim Kock, concerning a larger category of undirected graphs whose functor to modular operads is not just faithful but also full.

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Philip Hackney, Marcy Robertson, Donald Yau. 2019-06-04. Modular operads and the nerve theorem. https://doi.org/10.1016/j.aim.2020.107206

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