Localization of cofibration categories and groupoid $C^*$–algebras

Abstract

We prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an application we give a new construction of the functor that assigns to a groupoid its groupoid $C^{\ast }$–algebra and thereby its topological $K$–theory spectrum.