  We exhibit the cartesian differential categories of Blute, Cockett and Seely
as a particular kind of enriched category. The base for the enrichment is the
category of commutative monoids -- or in a straightforward generalisation, the
category of modules over a commutative rig $k$. However, the tensor product on
this category is not the usual one, but rather a warping of it by a certain
monoidal comonad $Q$. Thus the enrichment base is not a monoidal category in
the usual sense, but rather a skew monoidal category in the sense of
Szlach\'anyi. Our first main result is that cartesian differential categories
are the same as categories with finite products enriched over this skew
monoidal base.
  The comonad $Q$ involved is, in fact, an example of a differential modality.
Differential modalities are a kind of comonad on a symmetric monoidal
$k$-linear category with the characteristic feature that their co-Kleisli
categories are cartesian differential categories. Using our first main result,
we are able to prove our second one: that every small cartesian differential
category admits a full, structure-preserving embedding into the cartesian
differential category induced by a differential modality (in fact, a monoidal
differential modality on a monoidal closed category -- thus, a model of
intuitionistic differential linear logic). This resolves an important open
question in this area.
