Relative dendroidal Rezk nerve and applications

Kensuke Arakawa; Victor Carmona; Francesca Pratali

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arXiv · 2606.11895

Relative dendroidal Rezk nerve and applications

Kensuke Arakawa·Victor Carmona·Francesca Pratali

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Abstract

We extend the dendroidal Rezk nerve to the setting of relative $\infty$-operads. Our main theorem relates it to localization of $\infty$-operads, generalizing a theorem of Mazel-Gee. By exploiting the relation, we obtain a surprisingly effective tool to prove localization results in operadic contexts. As applications, we obtain a number of new results on operadic localizations, including a generalization of Willwacher's recent result on cyclic operads and operadic modules, and a description of locally constant factorization algebras on spheres in terms of discrete geometry.

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Kensuke Arakawa, Victor Carmona, Francesca Pratali. 2026-06-10. Relative dendroidal Rezk nerve and applications. https://arxiv.org/abs/2606.11895

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