Subject: followup on question
Date: Sat, 6 Apr 2002 09:47:08 +0100 (GMT Daylight Time)
From: Andrey Lazarev
To: Don Davis
Dear Don, cou you post this on the discussion list?
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Here's the follow-up on my original question.
Recall that the question was whether the functor F(?,X) converts
"finite" holimits to homotopy hocolimits in the category of spectra.
Or, more or less equivalently, when are "finite" holimits hocolimits?
However it is unclear is what "finite" means. I thought at first that
the indexing category should be finite with finitely many morphisms.
However it does not seem to be finite enough as actions of finite
groups make clear.
I now believe that the correct notion of finiteness here is that the
indexing category I is very small in the sense of Dwyer-Spalinsky.
That is, not only the set of morphisms and objects is finite, but
also the all morphisms go in the same direction, that is a long
enough string of morphisms must contain an identity morphism.
Can anyone confirm my belief/provide a reference?
Andrey
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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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