#### Volume 17, issue 5 (2017)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Localization of cofibration categories and groupoid $C^*$–algebras

### Markus Land, Thomas Nikolaus and Karol Szumiło

Algebraic & Geometric Topology 17 (2017) 3007–3020
##### 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.

##### Keywords
abstract and axiomatic homotopy theory, $K$–theory and operator algebras
Primary: 55U35
Secondary: 46L80