Abstract

The chain rule of Arone-Ching is a celebrated result in Goodwillie calculus and can be seen as a categorification of the chain rule from ordinary calculus. Given two functors from the category of spaces or spectra to itself, this chain rule describes how one can reconstruct the derivatives of the composite from the derivatives of the individual functors. Based on this result, Lurie conjectured the existence of such a chain rule for functors between a large class of ∞-categories. In joint work with Max Blans, we give an affirmative to Lurie’s conjecture. In this talk, I will give a brief introduction to Goodwillie calculus and discuss what such a chain rule should look like. I will then explain the main ideas that go into our proof and describe some potential applications to the theory of operads.