renamed the section in question fibrant and cofibrant objects and expanded further.

meanwhile Danny Stevenson writes in and points out various even stroger statements from the literature. Will try to include them after lunch...

]]>Danny Stevenson kindly wrote in to say that the fact in question

(that every simplicial presheaf that is degreewise a coproduct of representables is cofibrant in alll these model structures)

should be true and should be stated somewhere in Dan Dugger's work.

He indicates a proof which sounds very much along the lines of the proof that I did give.

So I regard this as settled for the time being, removed the green query boxes and just left in an indented remark that for the time being the proof is one I dreamed up which still deserves checking.

]]>I think I got it right now.

]]>now also added a section good covers with a definition that I think is good and with a proposition that I think is true and useful.

However, it seems at this point of the night I seem to be unable to write down precisely what in my head seems to be the obvious proof. I wrote down something there, but need to get back to it. Maybe I am wrong, but I am not convinced of that as yet ;-)

]]>a supposed proof that indeed we have a Quillen equivalence

is now

here in that entry

of course Diff and CartSp is just one specific example. In as far as the proof is correct, it will work for all such pairs, for instance Schemes vs AffineSchemes .

But check if it is indeed correct.

]]>I started a section

dependence on the underlying site at model structure on simplicial presheaves.

So far this quotes a result from Jardine's lectures and then looks a bit at an example.

At that example I would really like to conclude that the Quillen adjunction discussed there is actually a Quillen equivalence. But I have to interrupt now to make a telephone call... :-)

]]>