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Mar 8, 2012 at 15:32 comment added Fernando Muro Jacob, Tom, your arguments also show that the homotopy category of 1-connected spaces cannot be enhanced to a right pointed derivator. I just wanted to point this out in case somebody finds it interesting.
Mar 8, 2012 at 12:28 comment added Tom Goodwillie Thanks for the systematic answer. I realized also that, more simply, you can just write down a diagram of simply connected spaces whose usual holim is not simply-connected, apply the hypothetical $F$ and $G$ to it, and get a contradiction.
Mar 8, 2012 at 11:55 history answered Jacob Lurie CC BY-SA 3.0