Model categories 6 — Find conditions under which algebras over a noncofibrant operad admit a model structure that generaliz…

Find conditions under which algebras over a noncofibrant operad admit a model structure that generalize the monoid axiom of Schwede-Shipley. This would include the case where everything is fibrant, for example. Show that, under some more conditions, a weak equivalence of operads induces a Quillen equivalence of the algebra categories. Thus, sometimes you can use commutative, sometimes you can't, but you can always use E-infinity. And using E-infinity will not hurt you when you can use commutative.