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Jan 21, 2012 at 14:37 history edited David White CC BY-SA 3.0
Made it clear that the hypothesis actually implies both Hovey's unit axiom and the more general one
Jan 18, 2012 at 19:33 vote accept Fernando Muro
Jan 18, 2012 at 15:51 history edited David White CC BY-SA 3.0
added 319 characters in body
Jan 18, 2012 at 14:41 comment added David White At this link you can find an example where cofibrant objects are not flat. My gut says that if you tweak the example to be $T$-alg, then it'll be a monoidal model category and Hovey's unit axiom will hold. Since cofibrant objects are not flat, maybe this is a natural place to look for a counter-example to your claim. books.google.com/…
Jan 18, 2012 at 14:27 history answered David White CC BY-SA 3.0