$\infty$-Operads as Analytic Monads

Abstract

We develop an $\infty$-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 $\infty$-operads, namely $\infty$-operads as analytic monads. We justify this definition by proving that the $\infty$-category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for $\infty$-operads.

69 pages, v2: updated using results of arXiv:2002.01037, v3: accepted version

References in corpus (1)

• Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals

Cited by in corpus (7)

• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
• The $\infty$-Categorical Eckmann-Hilton Argument
• Decomposition spaces and restriction species
• On lax transformations, adjunctions, and monads in $(\infty ,2)$-categories
• The incidence comodule bialgebra of the Baez-Dolan construction
• On rectification and enrichment of infinity properads
• Types are Internal $\infty$-Groupoids