Title: Calculus III, Taylor series
Author: Thomas G. Goodwillie
Author's e-mail address: tomg@math.brown.edu

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 1-excisive in each
variable. We discuss some important examples, including the identity
functor and Waldhausen's algebraic K-theory.