Monoidal uniqueness of stable homotopy theory
Brooke Shipley

Abstract. We show that the monoidal product on the stable homotopy category
of spectra is essentially unique. This strengthens work of this author with
Schwede on the uniqueness of models of the stable homotopy theory of spectra.
Also, the equivalences constructed here give a unified construction of the
known equivalences of the various symmetric monoidal categories of spectra
(S-modules, W-spaces, orthogonal spectra, simplicial functors) with symmetric
spectra. As an application we show that with an added assumption about
underlying model structures Margolis' axioms uniquely determine the stable
homotopy category of spectra up to monoidal equivalence.