Calculus III: Taylor Series

By T. Goodwillie. 2003

192 citations recorded by the source corpus.

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 classied: 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.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aae83f4b187b6cf57750dc1ed6959f6a7641bef0

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In Computational Theory and Mathematics

1. John E. Harper
2. Kathryn Hess
3. Jacob Lurie
4. Carlos Simpson

In Mathematical Physics

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2. John E. Harper
3. Jacob Lurie
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Citations in the corpus

• Homotopy completion and topological Quillen homology of structured ring spectra (2011, background): “From now on in this paper, we assume that R is any commutative ring spectrum; i.e., we assume that R is any commutative monoid object in the category (SpΣ,⊗S , S) of symmetric spectra [39, 68].”
• (Infinity,2)-Categories and the Goodwillie Calculus I (2009, background): “(For a more comprehensive study of the Goodwillie calculus in the classical setting, we refer the reader to Goodwillie’s work ([20], [21], and [22]); see also [35] and [1] for a discussion of the chain rule).”