Harpaz's conjecture on the operadic nerve functor

Let OpKan\mathsf{Op}_{\mathrm{Kan}} be the category of Kan-enriched operads and let LQOp\mathsf{LQOp} be the category of Lurie quasioperads. Consider Lurie's operadic nerve functor

NLurie ⁣:OpKan→LQOp.N_{\mathrm{Lurie}}\colon\mathsf{Op}_{\mathrm{Kan}}\to\mathsf{LQOp}.

Harpaz's conjecture. The functor NLurieN_{\mathrm{Lurie}} induces an equivalence of ∞\infty-categories after localizing at weak equivalences.

The paper states that this long-standing conjecture has an affirmative answer as an application of its main theorem, so the conjecture is resolved.

References

Primary source

Kensuke Arakawa, Victor Carmona and Francesca Pratali, “Relative operads model -operads”, arXiv:2512.16374 (2025).

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