Cartesian differential categories revisited

Source abstract

We revisit the definition of Cartesian differential categories, showing that a slightly more general version is useful for a number of reasons. As one application, we show that these general differential categories are comonadic over categories with finite products, so that every category with finite products has an associated cofree differential category. We also work out the corresponding results when the categories involved have restriction structure, and show that these categories are closed under splitting restriction idempotents.