Tuesday, 23 April 2002
2:30 - 4:00  M Barr
             Absolute homology

Abstract
Call two maps, f,g: C --> C', of chain complexes absolutely homologous
if for any additive functor F, the induced Ff and Fg are homologous
(induce the same map on homology).  It is known that the identity is
absolutely homologous to 0 iff it is homotopic to 0 and tempting to
conjecture that f and g are absolutely homologous iff they are
homotopic (the "if" part is obvious).  This conjecture is false, but
there is an equational characterization of absolute homology.  I also
characterize left absolute and right absolute (in which F is
quantified over left or right exact functors).