Subject: Re: Ext question and conference
Date: 01 Jun 2003 18:43:32 -0400
From: Mark Hovey <hovey@picard.math.wesleyan.edu>
Reply-To: mhovey@wesleyan.edu
To: Don Davis <dmd1@lehigh.edu>

For the list:

Timo Hanke asks about "non-projective Ext".  For this to be generally
useful, I believe you should have a subbifunctor of Ext^1(-,-).  This is
the same thing as a proper class of short exact sequences, which is
covered in MacLane's homology book somewhere (its not in my hands at the
moment), and is closely related to relative homological algebra.
Examples include pure exact sequences, where one resolves an
arbitrary module by pure projectives, to get what is commonly denoted
as PExt.  Another example is if your category is chain complexes and you
consider dimensionwise split short exact sequences.  These proper
classes of short exact sequences occur in my paper on relating model
structures on abelian categories to "cotorsion theories"; this paper is
available on the Hopf archive in preprint form and has recently appeared
in Math. Zeitschrift 241 (2002) 553--592.
                Mark Hovey