Homotopy Theory for C^{*}-algebras

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.