Dendroidal sets as models for homotopy operads

By Denis-Charles Cisinski, Ieke Moerdijk. 2009

122 citations recorded by the source corpus.

The homotopy theory of ∞‐operads is defined by extending Joyal's homotopy theory of ∞‐categories to the category of dendroidal sets. We prove that the category of dendroidal sets is endowed with a model category structure, the fibrant objects of which are the ∞‐operads (that is, dendroidal inner Kan complexes). This extends the theory of ∞‐categories in the sense that the Joyal model category structure on simplicial sets, the fibrant objects of which are the ∞‐categories, is recovered from the model category structure on dendroidal sets by simply slicing over the monoidal unit.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e40680b20a8a0e96a9e5138776efa9de4e619a5f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Genuine equivariant operads (2017, background): “d X ∈ D ﬁbrant, LA → X is a weak equivalence iﬀ A → RX is. 9 The equivalence (1.16) generalizes the equivalence dSet⇄sOp● [15, Thm. 8.15], which culminates the project of Cisinski, Moerdijk, Weiss in [36, 37, 13, 14, 15]. Crucially, we note that, while the underlying categories in (1.16) are obtaine”
On the equivalence between Lurie's model and the dendroidal model for infinity-operads (2013, background): “Two approaches to the theory of higher operads will be discussed in this paper, namely Lurie’s theory of preoperads [28] and the theory of dendroidal sets [31, 11].”