Tangent categories, first defined by Jiří Rosický in 1984, are a categorical structure which allows one to abstractly work with and reason about many of the ideas in differential geometry. In this talk, I'll discuss how to define and work with Ehresmann connections in a tangent category. No prior knowledge of tangent categories or differential geometry will be assumed.
The content of the talk is based on joint work with Marcello Lanfranchi.