∞-Operads as Analytic Monads

Abstract

We develop an ∞ -categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for ∞ -operads, namely ∞ -operads as analytic monads. We justify this definition by proving that the ∞ -category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for ∞ -operads. © 2021 The Author(s). Published by Oxford University Press. All rights reserved.