A chain rule for Goodwillie derivatives of functors from spectra to spectra
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- by Michael Ching PDF
- Trans. Amer. Math. Soc. 362 (2010), 399-426 Request permission
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.References
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Additional Information
- Michael Ching
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 760391
- Received by editor(s): March 24, 2008
- Published electronically: July 2, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 399-426
- MSC (2000): Primary 55P42, 55P65
- DOI: https://doi.org/10.1090/S0002-9947-09-04834-X
- MathSciNet review: 2550157