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arXiv · 0812.0313

Splitting Monoidal Stable Model Categories

David Barnes
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Abstract

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.

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David Barnes. 2008-12-01. Splitting Monoidal Stable Model Categories. https://doi.org/10.1016/j.jpaa.2008.10.004

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