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

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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
##### Publication
Received: 28 October 2016
Revised: 2 May 2017
Accepted: 14 June 2017
Published: 19 September 2017
##### Authors
 Markus Land Mathematical Institute University of Regensburg Regensburg Germany http://www.markus-land.de Thomas Nikolaus Max Planck Institut für Mathematik Bonn Germany http://people.mpim-bonn.mpg.de/thoni/ Karol Szumiło Department of Mathematics University of Western Ontario London, ON Canada http://www-home.math.uwo.ca/~kszumilo/