A Chain Rule for Goodwillie Derivatives of Functors from Spectra to Spectra
نویسنده
چکیده
We prove a chain rule in the Goodwillie calculus of functors from spectra to spectra. We show that the derivatives of a composite FG at a base object X are given by taking the composition product of the derivatives of F at G(X) with the derivatives of G at X . Our proof also allows us to say something about the Taylor tower of FG (and not just its layers) in terms of the Taylor towers of F and G.
منابع مشابه
Functor Calculus and Operads March 13 – March 18 , 2011 MEALS
Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...
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