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