Global N∞$N_\infty$‐operads

Abstract

AbstractWe define ‐operads in the globally equivariant setting and completely classify them. These global ‐operads model intermediate levels of equivariant commutativity in the global world, that is, in the setting where objects have compatible actions by all compact Lie groups. We classify global ‐operads by giving an equivalence between the homotopy category of global ‐operads and the partially ordered set of global transfer systems, which are much simpler, algebraic objects. We also explore the relation between global ‐operads and ‐operads for a single group, recently introduced by Blumberg and Hill. One interesting consequence of our results is the fact that not all equivariant ‐operads can appear as restrictions of global ‐operads.