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. 
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     author = {Vladimir Hinich},
     title = {Rectification of algebras and modules},
     journal = {Documenta mathematica},
     pages = {879--926},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/508},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/508/}
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Vladimir Hinich. Rectification of algebras and modules. Documenta mathematica, Tome 20 (2015), pp. 879-926. doi: 10.4171/dm/508

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