Subject: RE: 2 questions
Date: Wed, 17 Mar 2004 09:02:15 -0000
From: "Neil Strickland" <N.P.Strickland@sheffield.ac.uk>
To: "Don Davis" <dmd1@lehigh.edu>

> Is the full subcategory of finite objects in the stable category
> equivalent, as a triangulated category, to a full subcategory of the
> derived category of an abelian category?  Can the abelian category be
> chosen to be symmetric monoidal and so that S^0 corresponds to a
> resolution of the unit object?

Let A be an abelian category, let X be an object of D(A), and let Y be
the cofibre of 2.1_X : X --> X.  One can then write down a nullhomotopy
of the map 2.1_Y.  However, if M is the mod 2 Moore spectrum then 2.1_M
is not nullhomotopic.  It follows that the stable homotopy category does
not embed in D(A).

Neil