A reference for Calculus of Functors for Model Categories I am wondering where I might look to see what has been done in terms of Calculus of Functors for more general weak equivalences and Model Categories.
I am at least aware of some of the extended definitions of the main concepts in Calculus of Functors to weak equivalence such as homotopy limits, but I was wondering if a document existed that worked through the basic of COF in this setting. 
I am aware also of Lurie's work here.(Thanks Harry for pointing this out.)
I appreciate your help.
 A: In Calculus III and its predecessors I studied functors from Top to Top and a few related cases. The ideas clearly generalize to functors $C\to D$ between model categories satisfying some pretty weak axioms, but I did not try to find the right axioms, and I don't think anyone has ever written anything definitive about that. 
Is that what you are asking about? 
The paper mentioned by Tilson takes the ideas in a somewhat different direction, I think: it's about treating the categories of functors themselves as model categories and finding Quillen adjoint pairs that refine my ideas.
A: I haven't read it, but maybe this could be useful: http://arxiv.org/abs/math/0601221
Calculus of Functors and Model categories by Biedermann Chorny and Roendigs
A: You might look at Thomas Goodwillie's papers "Calculus I" (K-Theory, 4), "Calculus II" (K-Theory, 5) and "Calculus III" (Geometry and Topology, 7).
A: You might look at http://arxiv.org/abs/1208.1919 "On calculus of functors in model categories, Stanculescu"
