Modular operads and the nerve theorem
arXiv:1906.01144 · doi:10.1016/j.aim.2020.107206
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 André Joyal and Joachim Kock, concerning a larger category of undirected graphs whose functor to modular operads is not just faithful but also full.
arXiv commentMinor changes
References in corpus (15)
- Dendroidal Sets
- 2-nerves for bicategories
- Monads with arities and their associated theories
- Homotopy theory for algebras over polynomial monads
- On an extension of the notion of Reedy category
- Infinity Properads and Infinity Wheeled Properads
- On the operad structure of admissible G-covers
- A graphical category for higher modular operads
- Dwyer--Kan homotopy theory for cyclic operads
- Higher cyclic operads
- A criterion for existence of right-induced model structures
- The 2-Chu-Dialectica construction and the polycategory of multivariable adjunctions
- On factorizations of graphical maps
- The modular envelope of the cyclic operad Ass
- Homotopy-coherent algebra via Segal conditions