Fixed-color equivariant simplicial operads admit model structures whose weak equivalences are detected by graph subgroups or by any chosen (G,Sigma)-family of subgroups.
Genuine equivariant operads
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abstract
We build new algebraic structures, which we call genuine equivariant operads, which can be thought of as a hybrid between equivariant 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.
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Homotopy theory of equivariant operads with fixed colors
Fixed-color equivariant simplicial operads admit model structures whose weak equivalences are detected by graph subgroups or by any chosen (G,Sigma)-family of subgroups.