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By a result of Schochet, the category of C*-algebras with homotopy equivalences and "Schochet fibrations" is a pointed category of fibrant objects whose homotopy category is the ordinary homotopy category of C*-algebras. It was observed by Andersen and Grodal that the above pointed category of fibrant objects is not the full subcategory of fibrant objects of a Quillen model category. Here is a recent reference reviewing both results: O. Uuye: Homotopy Theory for C*-algebras |
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By a result of Schochet, the category of C*-algebras with homotopy equivalences and "Schochet fibrations" is a pointed category of fibrant objects whose homotopy category is the ordinary homotopy category of C*-algebras. It was observed by Andersen and Grodal that the above pointed category of fibrant objects is not the full subcategory of fibrant objects of a Quillen model category. Here is a recent reference: O. Uuye: Homotopy Theory for C*-algebras |
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