Brown representability and flat covers

Henning Krause

Abstract. We exhibit a surprising connection between the following two 
concepts: Brown representability which arises in stable homotopy theory, and
flat covers which arise in module theory. It is shown that Brown 
representability holds for a compactly generated triangulated category if and
only if for every additive functor from the category of compact objects into
the category of abelian groups a flat cover can be constructed in a canonical
way. The proof also shows that Brown representability for objects and morphisms
is a consequence of Brown representability for objects and isomorphisms.