Some useful information is in Chacholski, Scherer, [Homotopy theory of diagrams][1], arxiv math/0110316 This and further references with useful material are listed in the reference section at <a href="http://ncatlab.org/nlab/show/homotopy+limit">nLab: homotopy limit</a>. (By immediate dualization this applies to homotopy colimits, of course). [1]: http://arxiv.org/abs/math/0110316