Appears in collection : Differential $\lambda$-Calculus and Differential Linear Logic, 20 Years Later / $ \lambda $-calcul différentiel et logique linéaire différentielle, 20 ans après

The calculus of homotopy functors is an important topological tool that has been used to shed light on and make connections between fundamental structures in homotopy theory and K-theory. It has also inspired the creation of new types of functor calculi to tackle problems in algebra and topology. In this talk, I will begin by describing properties that a functor calculus should have, before looking at a particular functor calculus, the abelian functor calculus, that has its origins in the work of Eilenberg, Mac Lane, Dold, and Puppe. Using this calculus, one can define the analog of a “directional derivative” for functors of abelian categories. I will describe how this directional derivative is used to create a cartesian differential category from abelian functor calculus, and if time permits, discuss some related work on connections between functor calculus and differential categories.