Subject: question about model categories
From: John Baez
Date: Mon, 7 May 2007 13:03:29 -0700
Thanks, Phil and Clemens! The paper by Rezk, Schwede, and Shipley
sounds very helpful, especially now that you've explained the fibrations,
cofibrations and weak equivalences in terms that a pedestrian can
understand.
Clemens Berger writes:
>> (3) It is of course some kind of folklore that topological spaces and
>> simplicial sets are interchangeable with respect to homotopy theory.
>> Nevertheless, it seems to me that John Baez' insistence of having
>> geometric model structures on simplicial spaces is justified, and this
>> topic is much less studied than the analogous one for bisimplicial
sets.
The folklore is fine as long as we really *can* interchange topological
spaces and simplicial sets. Otherwise it's a bit like this:
"It doesn't matter if you take a cheese sandwich or a ham sandwich;
they're equally good."
"Okay, I'll take a ham sandwich."
"No! Take a cheese sandwich - they're equally good."
One becomes suspicious...
Best,
jb