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

Abstract

We compare two approaches to the homotopy theory of ∞-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets and ∞-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 Γ. 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.