Homology, Homotopy and Applications
Volume 8 (2006)
Codescent theory II: cofibrant approximations
Pages: 211 – 242
We establish a general method to produce cofibrant approximations in the model category $U_S(C,D)$ of $S$-valued $C$-indexed diagrams with $D$-weak equivalences and $D$-fibrations. We also present explicit examples of such approximations. Here, $S$ is an arbitrary cofibrantly generated simplicial model category, and $D ⊂ C$ are small categories. An application to the notion of homotopy colimit is presented.
diagram category, cofibrant approximation, codescent
2010 Mathematics Subject Classification
Primary 18G55. Secondary 55U10.