A uniqueness theorem for stable homotopy theory. Math. Z. 239 (2002), no. 4, 803–828. In this paper the authors address the uniqueness of the stable homotopy category. Suppose C is a stable model category; this means that C is pointed and the suspension functor is a selfequivalence of the homotopy category of C. Then the homotopy category of C is triangulated and admits an action by the graded ring π∗S 0. The authors show that if the homotopy category of C has a small weak generator X such that [X, X] ∗ is isomorphic to π∗S 0 as a π∗S 0-module, then there is a Quillen equivalence from C to the Bousfield-Friedlander model category of spectra [A. K. Bousfield and E. M. Friedlander, in Geometric applications of homotopy theory (Proc. Conf.
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