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The W construction of Boardman and Vogt gives a cofibrant replacement for operads. In http://arxiv.org/abs/math/9907073, Salvatore describes a cofibrant replacement for algebras over an operad. Is there a similar construction which produces cofibrant resolutions of right or left modules over an operad? Does anyone have know of a reference for this?

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What do you mean by module over an operad? I've heard of modules over an algebra over an operad, and these have a model structure, so they have cofibrant replacement. Every operad is an algebra over a particular coloured operad, so if you take the model structure on modules over that algebra it should answer your question. References: ncatlab.org/nlab/show/…, arxiv.org/abs/math.CT/0701767 – David White May 30 '12 at 3:33
    
Nevermind, I found a reference which defines modules over an operad. It also kinda answers your question for left modules, since it produces a model structure on left modules over any non-$\Sigma$ operad and on some $\Sigma$-operads. This is John Harper's Homotopy Theory of Modules Over Operads. I'm not sure if it's what you wanted, since it's not very constructive: math.uwo.ca/~jharpe9/ModulesOperadsMonoidal.pdf – David White May 31 '12 at 14:01

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