One slightly displeasing thing about the theory of operads is that they are unable to encode the structure of inverses; e.g. the recognition principle for $n$-fold loop spaces says "there is an operad $E_n$ such that $E_n$-algebras which are also grouplike are homotopy equivalent to $n$-fold loop spaces." Have there been any attempts to describe a concept of "operad-with-inverse?" Alternately, are there some good reasons that attempting to augment an operad with inverses would cause the theory to collapse into an incomprehensible mess?
My primary reason for caring about this sort of thing is that I'm attempting to understand globular $\infty$-categories, in particular globular $\infty$-groupoids. The former can be understood as algebras over a certain globular operad, but the latter are described as "groupoidal" versions of the former. This is inconvenient because it is easier to work with the structure that (something like) an operad provides (rather than the mere property of being groupoidal) to do coherent constructions.
