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Mar 16, 2010 at 13:17 comment added David Carchedi P.S. I edited what I wrote because I was sloppy and was saying "Grothendieck fbration" when I meant "Grothendieck fibration in groupoids". The infinity-analogue to a general Grothendieck fibration is what Lurie calls a "Cartesian fibration."
Mar 16, 2010 at 13:13 history edited David Carchedi CC BY-SA 2.5
added 146 characters in body; deleted 2 characters in body
Mar 16, 2010 at 11:03 comment added David Carchedi No problem. I was also quite perplexed by the definition of the covariant (and contravariant) model structure when I first read it. It really doesn't make sense until you read about the straightening functor. (However, understanding why the straightening functor is the right thing to do, is also non-obvious in my opinion.)
Mar 16, 2010 at 3:24 comment added Harry Gindi I'm quite familiar with the ordinary case. Thanks for the other info though.
Mar 16, 2010 at 0:41 history answered David Carchedi CC BY-SA 2.5