ON A THEOREM OF BROWN AND ADAMS

Let J be the homotopy category of all spectra, J(c) subset of J the fu ll sub-category of finite spectra. Brown and Adams proved that any hom ological functor H:{J(c)}(op) --> Ab is the restriction of a represent able functor on J. Furthermore, any natural transformation is the rest riction of a map in J. One may naturally wonder whether this generaliz es to arbitrary triangulated categories, for instance D(R) where R is a ring. We show that the answer is in general no, although for R count able the generalization holds. Copyright (C) 1996 Elsevier Science Ltd