In algebraic topology, a branch of mathematics, the calculus of functors or Goodwillie calculus is a technique for studying functors by approximating them by a sequence of simpler functors; it generalizes the sheafification of a presheaf. This sequence of approximations is formally similar to the Taylor series of a smooth function, hence the term "calculus of functors".
Many objects of central interest in algebraic topology can be seen as functors, which are difficult to analyze directly, so the idea is to replace them with simpler functors which are sufficiently good approximations for certain purposes. The calculus of functors was developed by Thomas Goodwillie in a series of three papers in the 1990s and 2000s,[1][2][3] and has since been expanded and applied in a number of areas.