Geodesic
Rectification of algebras and modules
Documenta mathematica, Tome 20 (2015), pp. 879-926

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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. Rectification of algebras and modules. Documenta mathematica, Tome 20 (2015), pp. 879-926. doi: 10.4171/dm/508
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