Abstract

Goodwillie Calculus is a categorification of differential calculus in which infinity categories are the analogue of smooth manifolds, with functors between them the analogue of continuous/differentiable functions. Goodwillie’s main contribution is a tower of successive “n-polynomial” functor approximations, whose colimit converges to the original functor under the right circumstances. The analogy, which goes deep, gives insights into a topos-theoretic treatment of stable homotopy theory that is amenable to HoTT. In this approach, stabilizing a category is the analogue of linearizing it. We will give an exposition of Goodwillie calculus, covering polynomial approximations and stabilization.