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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Michael Ching
Journal: Trans. Amer. Math. Soc. 362 (2010), 399-426
MSC (2000): Primary 55P42, 55P65
Published electronically: July 2, 2009
MathSciNet review: 2550157
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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.


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Additional Information

Michael Ching
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04834-X
PII: S 0002-9947(09)04834-X
Received by editor(s): March 24, 2008
Published electronically: July 2, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.