Two models for the homotopy theory of ∞-operads

Abstract

We compare two models for (Formula presented.) -operads: the complete Segal operads of Barwick and the complete dendroidal Segal spaces of Cisinski and Moerdijk. Combining this with comparison results already in the literature, this implies that all known models for (Formula presented.) -operads are equivalent — for instance, it follows that the homotopy theory of Lurie's (Formula presented.) -operads is equivalent to that of dendroidal sets and that of simplicial operads.