Splitting monoidal stable model categories

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9 Citations (Scopus)

Abstract

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. 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 LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.
Original languageEnglish
Pages (from-to)846-856
Number of pages11
JournalJournal of Pure and Applied Algebra
Volume213
Issue number5
Early online date12 Nov 2008
DOIs
Publication statusPublished - May 2009

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