The Stable Homotopy Category Has a Unique Model at the Prime 2

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Spectra and symmetric spectra in general model categories (2000, background): “See also see [ 22 ] and [23] for uniqueness results for the usual stable homotopy category.”
Stable model categories are categories of modules (2003, background): “These uniqueness results are then developed further in [62] [55].”
Morita theory in abelian, derived and stable model categories (2003, background): “cient conditions for when a stable model category is Quillen equivalent to spectra – some of them in terms of the homotopy category and the natural action of the stable homotopy groups of spheres. In [Sch01b], this result is extended to a uniqueness theorem showing that the 2-local stable homotopy c”