Goodwillie calculus uses the intuition of calculus to approximate functors between categories by simpler functors. One such type of simpler functors are the “linear” functors. Linear functors are simple because they are determined in a weak sense by their coefficient spectra. A reduced homotopy functor is “linear” if it takes homotopy co-Cartesian squares to homotopy Cartesian squares (a property called 1-excisive). As we can generalize the notion of linear to the notion to being polynomial of degree at most \(n\), and this gives a better approximation, we generalize to \(n\)-excisive, and this gives a better approximation to the functor. The idea of \(n\)-excisive is to replace “squares” in the definition of 1-excisive with \(n\)-dimensional cubes. Then, in analogy with Taylor expansions, we can construct a resolution of the functor by a series of functors, \(P_n\) where each \(P_n\) is \(n\)-excisive. One application of this construction is to Waldhausen K-theory, from which the derivative gives Topological Hochschild homology.