Harpaz's conjecture on the operadic nerve functor

From papers

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 ⁣:OpKanLQOp.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.

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Sources & referencesView supporting material

Primary source

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

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