ScalingStacks

Proposition 5.9 ([F2]). Let $\mathcal{C}$ be a presentable symmetric monoidal $\infty$-category whose monoidal structure distributes over colimits.

To an $\mathcal{F}$-algebra $A$ in $\mathcal{C}$ there is functorially assigned associative algebra $U_{A}$ such that there is a canonical equivalence $\mathrm{Mod}_{A}^{\mathcal{F}}(\mathcal{C})\simeq\mathrm{Mod}_{U_{A}}(\mathcal{C})$ between $\mathcal{F}$-$A$-modules and left $U_{A}$-modules.

If $\mathcal{F}$ is the $\mathcal{E}_{n}$ operad, and the $\mathcal{E}_{n}$-algebra structure on $A$ is obtained by restriction from an $\mathcal{E}_{\infty}$-algebra structure, then there is a canonical equivalence of associative algebras $U_{A}\simeq S^{n-1}\otimes A$.