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

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An E∞E_{\infty} ring GG-category is a GG-category with an action by an E∞E_{\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 E∞E_{\infty} operad QG\mathcal{Q}_G. An E∞E_{\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 E∞E_{\infty} ring GG-categories to E∞E_{\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.

References

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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