Localization of Cofibration Categories and Groupoid $C^*$-algebras
  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. 
Markus Land, Thomas Nikolaus, Karol Szumi{\l}o
math.AT math.CT math.KT math.OA