%0 Journal Article
%T Calculus III: Taylor Series
%A Thomas G. Goodwillie
%J Mathematics
%D 2003
%I arXiv
%R 10.2140/gt.2003.7.645
%X 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.
%U http://arxiv.org/abs/math/0310481v1