On the equivalence between Lurie's model and the dendroidal model for infinity-operads

By Gijs Heuts, V. Hinich, Ieke Moerdijk. 2013

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We compare two approaches to the homotopy theory of infinity-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets and infinity-categories which replaces simplices by trees. The other is based on a certain homotopy theory of marked simplicial sets over the nerve of Segal's category Gamma. In this paper we prove that for operads without constants these two theories are equivalent, in the precise sense of the existence of a zig-zag of Quillen equivalences between the respective model categories.

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

View Paper: https://www.semanticscholar.org/paper/d1e3a7dbe365c9aa3aac14853f3e7ac6e46c688a

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Uniqueness of the multiplicative cyclotomic trace (2011, background): “…which yields a simplicial category [36, 2.1.1.22], and applying the homotopy coherent nerve to the resulting category yields an ∞ -operad provided that each morphism simplicial set of the multicategory is a Kan complex; consult [36, Proposition 2.1.1.27] for further discussion or see [30, §2].”