http://mathoverflow.net/questions/38911/a-reference-for-calculus-of-functors-for-model-categories
arXiv:1208.1919 On calculus of functors in model categories from arXiv Front: math.CT by Alexandru E. Stanculescu We present an analysis of some constructions and arguments from the universe of T. G. Goodwillie’s Calculus, in a general model theoretic setting.
nLab page on Calculus of functors