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.](http://www.math.harvard.edu/~lurie/papers/GoodwillieI.pdf)(Thanks Harry for pointing this out.)


I appreciate your help.



A reference for Calculus of Functors for Model Categories
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.


