Codescent theory II: cofibrant approximations

Abstract

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 subset C are small categories. An application to the notion of homotopy colimit is presented.