Infinite loop space machine for E-infinity ring G-categories

An EE_{\infty} ring GG-category is a GG-category with an action by an EE_{\infty} operad pair (PG,RG)(\mathcal{P}_G,\mathcal{R}_G) whose multiplicative action extends from RG\mathcal{R}_G to an action of the EE_{\infty} operad QG\mathcal{Q}_G. An EE_{\infty} ring GG-spectrum is the corresponding equivariant structured ring spectrum. Infinite loop space machine conjecture. There is an infinite loop space machine that carries EE_{\infty} ring GG-categories to EE_{\infty} ring GG-spectra. The proposed machine would extend the infinite loop space construction to the equivariant multiplicative setting; the source says that a proof is work in progress and seeks to avoid the categorical work in earlier constructions.

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Primary source

Bertrand Guillou and J. P. May, “Equivariant iterated loop space theory and permutative G-categories”, arXiv:1207.3459 (2017).

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