Paul Balmer, Michel Matthey
||Homology, Homotopy and Applications, 2006, Vol.8 (1), pp.211-242
We establish a general method to produce cofibrant approximations in the modelcategory U S (C,D) of S -valued C -indexed diagrams with D -weakequivalences and D -fibrations. We also present explicit examples of suchapproximations. Here, S is an arbitrary cofibrantly generated simplicialmodel category, and D subset C are small categories. Anapplication to the notion of homotopy colimit is presented.