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-algebras, KK-theory and E-theory, since all of these can be expressed as the homotopy theory of a category of fibrant objects.
Cite this article
Otgonbayar Uuye, Homotopical algebra for C*-algebras. J. Noncommut. Geom. 7 (2013), no. 4, pp. 981–1006DOI 10.4171/JNCG/141