The world of differential categories

Abstract: Differential categories use category theory to provide the foundations of differential calculus. In this talk, I will give you guided tour of the world of differential categories. We will see (1) differential categories, which give the algebraic foundations of differentiation; Cartesian differential categories, which give the foundations of multivariable differential calculus; and (3) tangent categories, which give the foundations of differential geometry. In particular we will look at the map of differential categories and see how these three concepts relate to each other. Moreover, the theory of differential categories has been successful in formalising various important concepts related to differentiation. In particular, this talk will set the table for next week’s talk, where Chiara Sava will explain how differential categories capture differential graded algebras.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)