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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.

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I don't think I agree with the addition of those two tags, but it matters little to me, so I will leave them. – B. Bischof Sep 16 '10 at 20:02
up vote 8 down vote accepted

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.

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@Tom This is exactly what I was looking for. I was hoping to "model"(ha ha) the style of the Goodwillie Calculus on Homotopy equivalences, to more general weak equivalences on some model categories. Thanks! – B. Bischof Sep 16 '10 at 15:26

I haven't read it, but maybe this could be useful: Calculus of Functors and Model categories by Biedermann Chorny and Roendigs

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Thanks, I did know of this, and forgot to put it in my question. It is in the direction I am wondering though, so thanks. – B. Bischof Sep 16 '10 at 2:41

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).

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You might look at "On calculus of functors in model categories, Stanculescu"

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