  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.
