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Higher categorical / operadic approach to homotopy associative, homotopy commutative, $H_\infty$ ring spectra?

Let $\mathcal C$ be a symmetric monoidal $\infty$-category, and let $O$ be an operad (for example, $O$ could be an $A_m$ or $E_n$ operad or a tensor product thereof, and $\mathcal C$ could be spaces ...
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