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

Understand

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.