Front: [arXiv:0710.5567] A chain rule for Goodwillie derivatives of functors from spectra to spectra

Fri, 9 May 2008
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arXiv:0710.5567

Title: A chain rule for Goodwillie derivatives of functors from spectra to spectra
Authors: Michael Ching
Categories: math.AT Algebraic Topology
Comments: 29 pages, LaTeX; considerably expanded section 6 to provide a correct proof of 6.1, other sections rewritten to improve exposition but no major changes; submitted for publication
MSC: 55P42; 55P65

Abstract: We prove a chain rule for the Goodwillie calculus of functors from spectra to spectra. We show that the (higher) derivatives of a composite functor $FG$ at a base object $X$ are given by taking the composition product (in the sense of symmetric sequences) of the derivatives of $F$ at $G(X)$ with the derivatives of $G$ at $X$. We also consider the question of finding $P_n(FG)$, and give an explicit formula for this when $F$ is homogeneous.

Owner: Michael Ching
Version 1: Tue, 30 Oct 2007 03:28:11 GMT
Version 2: Wed, 31 Oct 2007 13:58:36 GMT
Version 3: Sun, 23 Mar 2008 04:43:05 GMT

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