Rectification of algebras and modules

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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.

Original languageEnglish
Pages (from-to)879-926
Number of pages48
JournalDocumenta Mathematica
Issue number2015
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics (all)


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