In 1-categorical algebra one knows that, in a locally presentable category, every algebra for a finite product theory is a colimit of free algebras. Is the same true for algebras of finite product theories in presentable $\infty$-categories? I would already be content to know this for $E_\infty$-algebras and modules over a fixed $E_\infty$-algebra in a presentable $\infty$-category. Thanks!
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