Subject: Re: question & response
Date: Fri, 05 Apr 2002 09:41:28 -0500
From: John Klein <klein@turing.math.wayne.edu>
Organization: Wayne State University
To: Don Davis <dmd1@lehigh.edu>

Here is an argument for Andrey's question:

1) When I is the category a -> c <- b
then holim G is then the homotopy pullback. The result is
true in this case (it amounts to the fact that a
homotopy pullback is also a homotopy pushout
in the category of spectra).

2) Any finite homotopy limit can be expressed as a finitely
iterated homotopy pullback (using the skeleta of the nerve of I).

John

> __________________________________________________
>
> Subject: question for the discussion list
> Date: Thu, 4 Apr 2002 16:41:44 +0100 (GMT Daylight Time)
> From: Andrey Lazarev <A.Lazarev@bristol.ac.uk>
>
> Here's a question for the discussion list:
>
> Let I be a category with finitely many objects and and
> finitely many morphisms and G:I-->Spec a functor from I into the
> category of spectra.
>
> Let X be another spectrum. Then there is a map
> hocolim F(G(?),X)-->F(holim(G),X). Here F stands for the function
> spectrum.
>
> Question: is it true that this map is a weak equivalence? If not what
> further restrictions should one put on I ensuring that this is an
> eqivalence?
>
>