  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 Cartesian categories, so that every Cartesian category 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.
