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arXiv · 2512.16374

Relative operads model $\infty$-operads

Kensuke Arakawa·Victor Carmona·Francesca Pratali
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Abstract

Given a (colored) operad and a set of unary operations, we can form an associated $\infty$-operad via localization. We show that localization determines an equivalence of homotopy theories of relative operads and $\infty$-operads. As an application, we give an affirmative answer to an open question by Harpaz, proving that Lurie's operadic nerve functor determines an equivalence of homotopy theories of simplicial operads and Lurie's $\infty$-operads.

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Kensuke Arakawa, Victor Carmona, Francesca Pratali. 2025-12-18. Relative operads model $\infty$-operads. https://arxiv.org/abs/2512.16374

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