BROWN REPRESENTABILITY FOR THE DUAL

Let J be the homotopy category of all spectra. Brown proved that a hom ological functor H : J(op) --> Ab is representable if it takes coprodu cts to products. That is, the functors [-,h] may be characterised as t he homological functors taking coproducts to products. In this article , we will prove the dual. A covariant functor H : J --> Ab which takes products to products is representable; it is of the form [h,-].