Key points are not available for this paper at this time.
Let O be a topological (colored) operad. The Lurie -category of O -algebras with values in (-category of) complexes is compared to the -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.
Vladimir Hinich (Thu,) studied this question.