∞-Operads as Analytic Monads

David Gepner, Rune Haugseng*, Joachim Kock

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)12516-12624
Number of pages109
JournalInternational Mathematics Research Notices
Issue number16
Publication statusPublished - 1 Aug 2022


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