On the chain rule in Goodwillie calculus

The chain rule of Arone-Ching is a celebrated result in Goodwillie calculus, describing how the derivatives of a composite of two functors between spaces or spectra can be reconstructed from the derivatives of the individual functors. Based on this result, Lurie conjectured that such a chain rule should more generally hold for a large class of $\infty$-categories. In this talk, I will discuss recent joint work with Max Blans in which we give an affirmative answer to this conjecture.