If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit S forms a commutative ring. An idempotent e of this ring will split the homotopy category. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to the product of C localised at the object eS and C localised at the object (1-e)S. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

The stable homotopy category of spectra was created to capture those phenomena which are "stable". I will motivate the interest in this category by giving examples of stable phenomena, including generalized cohomology theories, Steenrod operations, the Freudenthal suspension theorem, Spanier-Whitehead duality and cobordism.