We construct an equivariant infinite loop space machine denned on certain class of monoidal OG-categories which have built-in Mackey structure. Applications include the equivariant infinite delooping of the classifying space BF(G) for stable spherical G-fibrations and also the construction of an infinite loop G-space E(X, G) with π0HE(X, G) naturally isomorphic to the equivariant Whitehead groups WhH(X) of given G-space X.
- Mackey system of monoidal categories
- equivariant Whitehead group
- spherical G-fibration
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