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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–algebra and thereby its topological K–theory spectrum.

Keywords
abstract and axiomatic homotopy theory, $K$–theory and operator algebras
Mathematical Subject Classification 2010
Primary: 55U35
Secondary: 46L80
References
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/