#### Geometry & Topology, Vol. 7 (2003)
Paper no. 19, pages 645--711.

## Calculus III: Taylor Series

### Thomas G Goodwillie

**Abstract**.
We study functors from spaces to spaces or spectra that preserve weak
homotopy equivalences. For each such functor we construct a universal
n-excisive approximation, which may be thought of as its n-excisive
part. Homogeneous functors, meaning n-excisive functors with trivial
(n-1)-excisive part, can be classified: they correspond to symmetric
functors of n variables that are reduced and 1-excisive in each
variable. We discuss some important examples, including the identity
functor and Waldhausen's algebraic K-theory.
**Keywords**.
Homotopy functor, excision, Taylor tower

**AMS subject classification**.
Primary: 55P99.
Secondary: 55U99.

**DOI:** 10.2140/gt.2003.7.645

**E-print:** `arXiv:math.AT/0310481`

Submitted to GT on 8 November 2002.
Paper accepted 20 October 2003.
Paper published 28 October 2003.

Notes on file formats
Thomas G Goodwillie

Department of Mathematics, Brown University

Box 1917, Providence RI 02912-0001, USA

Email: tomg@math.brown.edu

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