Modular operads and the nerve theorem
Category Theory
2020-07-03 v2 Algebraic Topology
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.
Cite
@article{arxiv.1906.01144,
title = {Modular operads and the nerve theorem},
author = {Philip Hackney and Marcy Robertson and Donald Yau},
journal= {arXiv preprint arXiv:1906.01144},
year = {2020}
}
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