Gutiérrez Marín, Javier J.White, David2023-03-012023-03-0120181472-2747https://hdl.handle.net/2445/194371We prove a conjecture of Blumberg and Hill regarding the existence of $N_{\infty}$-operads associated to given sequences $\mathcal{F}=\left(\mathcal{F}_n\right)_{n \in \mathbb{N}}$ of families of subgroups of $G \times \Sigma_n$. For every such sequence, we construct a model structure on the category of $G-$ operads, and we use these model structures to define $E_{\infty}^{\mathcal{F}}$-operads, generalizing the notion of an $N_{\infty}$-operad, and to prove the Blumberg-Hill conjecture. We then explore questions of admissibility, rectification, and preservation under left Bousfield localization for these $E_{\infty}^{\mathcal{F}}$-operads, obtaining some new results as well for $N_{\infty}^{-}$ operads.44 p.application/pdfeng(c) Mathematical Sciences Publishers, 2018Teoria de l'homotopiaTeoria de modelsHomotopy theoryModel theoryinfo:eu-repo/semantics/article6822392023-03-01info:eu-repo/semantics/openAccess