Goodwillie calculus and operads

Abstract: The goal of this talk is to survey the role of operads in Goodwillie’s calculus of functors. A key observation is that the derivatives of the identity functor, on a suitable pointed $\infty$-category $C$, admit an operad structure which in the case of pointed spaces recovers a spectral version of the Lie operad. I will give a couple different ways to construct the operad structure in general, and then focus on the case where $C$ is itself the $\infty$-category of algebras over some (stable, non-unital) operad $P$. In that case, the derivatives of the identity functor on $C$ recover, in some form, the operad $P$.

algebraic topologycategory theoryquantum algebra

Audience: learners

operad pop-up