  We extend to general Cartesian categories the idea of Coherent
Differentiation recently introduced by Ehrhard in the setting of categorical
models of Linear Logic. The first ingredient is a summability structure which
induces a partial left-additive structure on the category. Additional
functoriality and naturality assumptions on this summability structure
implement a differential calculus which can also be presented in a formalism
close to Blute, Cockett and Seely's Cartesian differential categories. We show
that a simple term language equipped with a natural notion of differentiation
can easily be interpreted in such a category.
