Equivalence of comparison functors between equivariant operads and G-∞-operads

Determine whether the genuine operadic nerve and related comparison functors that relate equivariant topological operads and their algebras to G-∞-operads and their ∞-categorical algebras are equivalences of the associated homotopy or ∞-categories for finite groups G.

Background

The paper discusses two parallel formalisms for operads—equivariant topological operads and G-∞-operads—and notes the existence of comparison (nerve) functors connecting them. While such comparisons are well-understood in certain non-equivariant settings, their status in the equivariant context is less settled.

Specifically, even with assumptions on the operads, it is not established that these comparison functors are equivalences. Resolving this would clarify the relationship between topological and ∞-categorical models of equivariant operadic structures and their algebras.