A reference for Calculus of Functors for Model Categories - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T22:08:02Z http://mathoverflow.net/feeds/question/38911 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/38911/a-reference-for-calculus-of-functors-for-model-categories A reference for Calculus of Functors for Model Categories B. Bischof 2010-09-16T01:44:35Z 2010-09-17T00:04:43Z <p>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.</p> <p>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. </p> <p>I am aware also of Lurie's work <a href="http://www.math.harvard.edu/~lurie/papers/GoodwillieI.pdf" rel="nofollow">here.</a>(Thanks Harry for pointing this out.)</p> <p>I appreciate your help.</p> http://mathoverflow.net/questions/38911/a-reference-for-calculus-of-functors-for-model-categories/38916#38916 Answer by Sean Tilson for A reference for Calculus of Functors for Model Categories Sean Tilson 2010-09-16T02:36:35Z 2010-09-16T02:36:35Z <p>I haven't read it, but maybe this could be useful: <a href="http://arxiv.org/abs/math/0601221" rel="nofollow">http://arxiv.org/abs/math/0601221</a> Calculus of Functors and Model categories by Biedermann Chorny and Roendigs</p> http://mathoverflow.net/questions/38911/a-reference-for-calculus-of-functors-for-model-categories/38929#38929 Answer by Michael A Warren for A reference for Calculus of Functors for Model Categories Michael A Warren 2010-09-16T05:27:46Z 2010-09-16T05:27:46Z <p>You might look at Thomas Goodwillie's papers "Calculus I" (<em>K-Theory</em>, 4), "Calculus II" (<em>K-Theory</em>, 5) and "Calculus III" (<em>Geometry and Topology</em>, 7).</p> http://mathoverflow.net/questions/38911/a-reference-for-calculus-of-functors-for-model-categories/38957#38957 Answer by Tom Goodwillie for A reference for Calculus of Functors for Model Categories Tom Goodwillie 2010-09-16T10:46:57Z 2010-09-17T00:04:43Z <p>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. </p> <p>Is that what you are asking about? </p> <p>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.</p>