A chain rule for Goodwillie derivatives of functors from spectra to spectra

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A Chain Rule for Goodwillie Derivatives of Functors from Spectra to Spectra

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.

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ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 2009

ISSN: 0002-9947

DOI: 10.1090/s0002-9947-09-04834-x