Homotopical algebra for C*-algebras

Abstract

The 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${}^{\ast }$-algebras, KK-theory and E-theory, since all of these can be expressed as the homotopy theory of a category of fibrant objects.