We build new algebraic structures, which we call genuine equivariant operads and which can be thought of as a hybrid between operads and coefficient systems. We then prove an Elmendorf-Piacenza type theorem stating that equivariant operads, with their graph model structure, are equivalent to genuine equivariant operads, with their projective model structure.

As an application, we build explicit models for the $N_{\infty }$-operads of Blumberg and Hill.

中文翻译：

---

真正的等变运算符

我们建立了新的代数结构，我们称其为真正的等变运算符，可以将其视为运算符和系数系统的混合体。然后，我们证明Elmendorf-Piacenza型定理，说明等变量算符及其图模型结构等效于真正的等变量算符及其射影模型结构。

作为应用程序，我们为 ${ñ}_{\infty }$-布隆伯格和希尔的歌剧。