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Which positive flat stable model structures on (flavors of) spectra have the property that cofibrant operad-algebras forget to cofibrant spectra?

I asked this question over a year ago, when revising my paper (joint with Donald Yau) Smith Ideals of Operadic Algebras in Monoidal Model Categories. In the end, I thought this question was relevant ...
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When is the cofibrant replacement of a product the product of the cofibrant replacements?

I asked this question a very long time ago, when I was just starting to do research in abstract homotopy theory. This is a classic case of an xy problem, where I had a proof in mind, and by asking ...
David White's user avatar
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