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