AUTHOR: Apostolos Beligiannis

ADDRESS: Department of Mathematics,
         University of the Aegean,
         83200 Karlovassi, Samos, Greece.

ABSTRACT: Our  aim in this paper is to develop a theory of purity
and to prove in a unified conceptual way the existence of almost
split morphisms, almost split sequences and almost split triangles
in Abstract Homotopy Categories, a rather omnipresent class of
categories of interest in representation theory. Our main tool for
doing this is the classical  Brown Representability Theorem.

CURRENT STATUS: Preprint.
                To appear in Algebras and Representation Theory.