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

DOI:
https://doi.org/10.1090/S0002-9947-09-04834-X

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 at a base object are given by taking the composition product (in the sense of symmetric sequences) of the derivatives of at with the derivatives of at . We also consider the question of finding , and give an explicit formula for this when is homogeneous.

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Additional Information

**Michael Ching**

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

DOI:
https://doi.org/10.1090/S0002-9947-09-04834-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.