Subject: Re: 3 postings
Date: Mon, 19 Jan 2004 14:11:15 -0500 (EST)
From: Nora Ganter <nora@math.mit.edu>
To: Don Davis <dmd1@lehigh.edu>

Strictly speaking, in this case it is not really a colimit, but its
derived functor: it is left adjoint to the constant diagram functor
  Ho(C) ---> Ho(C^I),
but the forgetfull functor Ho(C^I) ---> Ho(C)^I is not normally an
equivalence of categories.
The question under which circumstances such model structures exist, was
first discussed by C. Reedy in an unpublished preprint that you
can find on Phil Hirschhorn's webpage:

www.math-mit.edu/~psh/#Reedy

I think I have also seen it in Marc Hovey's
book on model categories with a reference to Dwyer-Hirschhorn-Kan.
(Also on Phil's webpage)

>
> Subject: reference needed
> Date: Mon, 19 Jan 2004 10:14:59 +0100
> From: Gaucher Philippe <Philippe.Gaucher@pps.jussieu.fr>
>
> Question for the mailing-list:
>
> Could I have please a reference for the general fact (if this is true !)
> that
> the homotopy colimit is a colimit in Ho(C) where C is a model category ?
> If
> for any given small category I, there exists a model structure on C^I
> such
> that the constant diagram functor is a right Quillen functor, it's OK
> (for
> example if C is cofibrantly generated). Same question for the homotopy
> limit.
>
> pg.
>
>