Acta Mathematica Universitatis Comenianae
Cofibration in the category of noncommutative CW complexes is defined. The C*-algebraic counterparts of topological mapping Cylinder and mapping cone are presented as examples of noncommutative CW complex cofibres. As a generalization, the concepts of noncommutative mapping cylindrical and conical telescope are introduced to provide more examples of NCCW complex cofibres. Their properties and K-theoretic behavior are also studied in detail. We will see that they carry the properties similar to the topological properties of their CW complex counterparts.
"Cofibrations in the Category of Noncommutative CW Complexes",Vida Milani, Seyed M.H. Mansourbeigi and Ali-Asghar Rezaei, Acta Mathematica Universitatis Comenianae, vol. 85 No.1 (2016).