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Is there a model structure for S-modules such that cofibrant operad-algebras forget to cofibrant S-modules?

Here is something that I think is reasonably difficult to get around. As you observe, the unit is the initial object of commutative monoids, and so your request includes that the unit is cofibrant. ...
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1 vote

Operad terminology - Operads with and without O(0).

A 2020 paper Operads, monoids, monads, and bar constructions by Ruozi Zhang, Foling Zou, and J.P. May revisits the foundations of operad theory and discusses several possible choices for what $\...
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1 vote

Operad terminology - Operads with and without O(0).

EDIT: I did not realize there was still controversy, and I didn't know about the 2020 paper Peter May linked to today, but I like it a lot. I'm always happy to defer to Peter, so the terminology I'll ...
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