Genuine Equivariant Operads
A classic result by Elmendorf states that G-spaces and G-coefficient systems are Quillen equivalent. Moreover, this result remains true if one replaces spaces with other well-behaved categories (including simplicial sets and categories). However, when considering G-operads, this equivalence fails to capture certain desired subtleties. In this talk, I will introduce (G-)operads and review this failure. I will then define a new algebraic gadget called genuine G-operads (playing the role of coefficient systems), and state an Elmendorf-type result in this context. This is joint work with L. Pereira.