English

$\infty$-Operads as Analytic Monads

Algebraic Topology 2020-10-30 v3 Category Theory

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.

Keywords

Cite

@article{arxiv.1712.06469,
  title  = {$\infty$-Operads as Analytic Monads},
  author = {David Gepner and Rune Haugseng and Joachim Kock},
  journal= {arXiv preprint arXiv:1712.06469},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-22T23:21:45.424Z