Brown representability for the dual (Q1127771)

Let \({\mathcal T}\) be the homotopy category of all spectra and \({\mathcal A}b\) the category of abelian groups. The author dualizes Brown's theorem [\textit{E. H. Brown}, Ann. Math., II. Ser. 75, 467-484 (1962; Zbl 0101.40603)] and shows that a (covariant) homological functor \(H : {\mathcal T}\to {\mathcal A}b\) which respects products is representable.