Dendroidal sets and simplicial operads
By Denis-Charles Cisinski, Ieke Moerdijk. 2011
135 citations recorded by the source corpus.
We establish a Quillen equivalence relating the homotopy theory of Segal operads and the homotopy theory of simplicial operads, from which we deduce that the homotopy coherent nerve functor is a right‐Quillen equivalence from the model category of simplicial operads to the model category structure for ∞‐operads on the category of dendroidal sets. By slicing over the monoidal unit, this also gives the Quillen equivalence between Segal categories and simplicial categories proved by Bergner, as well as the Quillen equivalence between quasi‐categories and simplicial categories proved by Joyal and Lurie. We also explain how this theory applies to the usual notion of operad (that is, with a single colour) in the category of spaces.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c0ec86b2f9754f1c45c13b6a0178f5aa5bf81de9
How researchers see this paper
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In Algebra and Number Theory
- L. Pereira
- P. Bonventre
- V. Hinich
- Gijs Heuts
- Ieke Moerdijk
- Benoit Fresse
- Joachim Kock
- Denis-Charles Cisinski
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the equivalence between Lurie's model and the dendroidal model for infinity-operads (2013, methodology): “The equivalence of the latter two approaches has already been shown in [13].”
- Genuine equivariant operads (2017, methodology): “In the next major step of the project, we intend to connect the two papers by generalizing the main theorem of Cisinski and Moerdijk in [5] and showing the existence of a Quillen equivalence”