%0 Journal Article
%T Splitting Monoidal Stable Model Categories
%A David Barnes
%J Mathematics
%D 2008
%I arXiv
%R 10.1016/j.jpaa.2008.10.004
%X 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.
%U http://arxiv.org/abs/0812.0313v1