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:
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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)?
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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.
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Andrey Lazarev
A.Lazarev@bristol.ac.uk
Phone +44 117 928 7997
School of Mathematics
University of Bristol
Bristol BS8 1TW UK
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