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Localization of
cofibration categories and groupoid $C^*$–algebras
Markus Land, Thomas Nikolaus and Karol Szumiło |
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Algebraic & Geometric Topology 17 (2017) 3007–3020
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Abstract |
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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 –algebra and thereby its topological –theory spectrum. |
Keywords
abstract and axiomatic homotopy theory, $K$–theory and
operator algebras
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Mathematical Subject Classification 2010
Primary: 55U35
Secondary: 46L80
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References |
Publication
Received: 28 October 2016
Revised: 2 May 2017
Accepted: 14 June 2017
Published: 19 September 2017
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Authors |
| Markus Land | |
| Mathematical Institute University of Regensburg Regensburg Germany |
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| http://www.markus-land.de | |
| Thomas Nikolaus | |
| Max Planck Institut für
Mathematik Bonn Germany |
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| http://people.mpim-bonn.mpg.de/thoni/ | |
| Karol Szumiło | |
| Department of Mathematics University of Western Ontario London, ON Canada |
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| http://www-home.math.uwo.ca/~kszumilo/ | |
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