We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal –excisive approximation, which may be thought of as its –excisive part. Homogeneous functors, meaning –excisive functors with trivial –excisive part, can be classified: they correspond to symmetric functors of variables that are reduced and –excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen’s algebraic –theory.
"Calculus III: Taylor Series." Geom. Topol. 7 (2) 645 - 711, 2003. https://doi.org/10.2140/gt.2003.7.645