The past, present, and future of tangent categories

This will be a survey talk consisting of three parts. In the first part, we’ll look at what a tangent category is, and how the concept has developed. In the second part, we’ll give an overview of some of the key ideas and definitions in tangent category theory, and how they give new perspectives on aspects of differential geometry. In the third part, we’ll look at avenues for future work in this area.