Abstract
Category of fibrant objects is a convenient framework to do homotopy theory, introduced and developed by Ken Brown. In this paper, we apply it to the category of C^{*}-algebras. In particular, we get a unified treatment of (ordinary) homotopy theory for C^{*}-algebras, KK-theory and E-theory, as all of these can be expressed as the homotopy category of a category of fibrant objects.
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