Jean-Simon Lemay (University of Oxford (UK)), Differential Algebras for Differential Categories



Differential categories were introduced by Blute, Cockett, and Seely to categorify Ehrhard and Regnier's differential linear logic and the differential lambda calculus. Since then, differential categories have lead to abstract formulations of many notions involving differentiation such as the directional derivative, differential forms, smooth manifolds, De Rham cohomology, etc. Therefore, if the theory of differential categories wishes to champion itself as axiomatizing the fundamentals of differentiation: differential algebras should fit naturally in this story. In this talk, we give an overview of the story of differential categories and introduce T-differential algebras, which are generalization of differential algebras for differential categories. We also discuss free and cofree T-differential algebras, and power series for differential categories.