Subject: comment on Goodwillie's responses Date: Mon, 8 Apr 2002 15:06:44 +0100 (GMT Daylight Time) From: Andrey Lazarev To: dmd1@lehigh.edu Goodwillie writes: ----------------------------------------------------------------- I don't know any references. Which reminds me, does anybody have a reference for the fact that holim over a very small category commutes (up to weak equivalence) with hocolim over a filtering category (or a directed set)? ----------------------------------------------------------------- I presume the question here is about ho(co)limits of spaces rather than spectra. I found the following reference: R.Vogt, Commuting homotopy limits. Math. Z. 153 (1977), no. 1, 59--82. It is proved there that homotopy pullbacks of spaces commute with hocolimits along a directed set. --------------------------------------- Andrey Lazarev A.Lazarev@bristol.ac.uk Phone +44 117 928 7997 School of Mathematics University of Bristol Bristol BS8 1TW UK ---------------------------------------