We start with the defiition of a stable homotopy category (SHC) and try to construct one for the category of p-complete abelian groups (Ab_p). Homology functors play an important role in this process so we consider possible candidates. We find that the unusual properties of Ab_p complicate the standard homology functors and in fact reduce many familiar examples to the trivial functor. We will show that there exists no homology functors that extend standard homology thereby suggesting the SHC is 0. i |