Let O be a topological (colored) operad. The Lurie infinity-category of O-algebras with values in (infinity-category of) complexes is compared to the infinity-category underlying the model category of (classical) dg O-algebras. This can be interpreted as a rectification result for Lurie operad algebras. A similar result is obtained for modules over operad algebras, as well as for algebras over topological PROPs.
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