Algebraic & Geometric Topology

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

Markus Land, Thomas Nikolaus, and Karol Szumiło

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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.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 5 (2017), 3007-3020.

Dates
Received: 28 October 2016
Revised: 2 May 2017
Accepted: 14 June 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841490

Digital Object Identifier
doi:10.2140/agt.2017.17.3007

Mathematical Reviews number (MathSciNet)
MR3704250

Zentralblatt MATH identifier
06791391

Subjects
Primary: 55U35: Abstract and axiomatic homotopy theory
Secondary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

Keywords
abstract and axiomatic homotopy theory $K$–theory and operator algebras

Citation

Land, Markus; Nikolaus, Thomas; Szumiło, Karol. Localization of cofibration categories and groupoid $C^*$–algebras. Algebr. Geom. Topol. 17 (2017), no. 5, 3007--3020. doi:10.2140/agt.2017.17.3007. https://projecteuclid.org/euclid.agt/1510841490


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