The chain rule in Goodwillie calculus

Abstract

Goodwillie calculus assigns to every reduced finitary functor between differentiable categories a sequence of derivatives. For functors on the category of pointed spaces or spectra, Arone and Ching showed that these derivatives satisfy a chain rule. Lurie conjectured that such a chain rule holds in much greater generality. The main purpose of this thesis is to give a proof – found in collaboration with Thomas Blom – of this conjecture. The key step in the argument is the construction of a lax monoidal structure on the Goodwillie derivatives functor.