On the equivalence of the Lurie's $\infty$-operads and dendroidal $\infty$-operads

Ieke Moerdijk; Vladimir Hinich

On the equivalence of the Lurie's $\infty$-operads and dendroidal $\infty$-operads

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arxiv 2206.14033 v3 pith:UIG3HTCH submitted 2022-06-28 math.CT math.AT

Vladimir Hinich , Ieke Moerdijk This is my paper · ORCID

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keywords inftyoperadsdendroidalequivalenceluriealgebraalteredbook

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abstract

In this paper we prove the equivalence of two symmetric monoidal $\infty$-categories of $\infty$-operads, the one defined in Lurie's book on Higher Algebra and the one based on dendroidal spaces. V.2 Some corrections made and exposition slightly altered.

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The root functor
math.AT 2025-05 conditional novelty 7.0 of 10

Every normal dendroidal ∞-operad is an operadic weak equivalence to the localization at root-preserving maps of the nerve of its discrete, Σ-free operad of elements.

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