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Apr 16, 2011 at 1:07 comment added Akhil Mathew Dear David, thanks! I've started reading Cisinski, though it's probably going to take some time to get far in it.
Apr 15, 2011 at 8:19 comment added Jonathan Chiche I think the emphasis on presheaf models is due to the difficulty of the general case! This is explained in the introduction of Maltsiniotis's book.
Apr 15, 2011 at 6:50 history edited David Roberts CC BY-SA 3.0
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Apr 15, 2011 at 6:48 comment added David Roberts Ah, that would explain the emphasis on presheaf models, where the cofibrations are taken to be monomorphisms.
Apr 15, 2011 at 6:44 comment added Tim Porter Point of Info: Grothendieck actually did not like Thomason's structure as the cofibrations worried him.
Apr 15, 2011 at 6:32 comment added David Roberts Thanks, Theo. I knew they were available electronically somewhere - just not from Cisinski's home page!
Apr 15, 2011 at 5:47 comment added Theo Buehler All the relevant papers can be found on Maltsiniotis' homepage: math.jussieu.fr/~maltsin/ps.html
Apr 15, 2011 at 5:15 history answered David Roberts CC BY-SA 3.0