We establish a general method to produce cofibrant approximations in the model category US(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.
Homology, Homotopy and Applications, Vol. 8 (2006), No. 1, pp.211-242.
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