We prove a conjecture of Blumberg and Hill regarding the existence of –operads associated to given sequences of families of subgroups of . For every such sequence, we construct a model structure on the category of –operads, and we use these model structures to define –operads, generalizing the notion of an –operad, and to prove the Blumberg–Hill conjecture. We then explore questions of admissibility, rectification, and preservation under left Bousfield localization for these –operads, obtaining some new results as well for –operads.
"Encoding equivariant commutativity via operads." Algebr. Geom. Topol. 18 (5) 2919 - 2962, 2018. https://doi.org/10.2140/agt.2018.18.2919