一句话：提出笛卡尔差分范畴，统一笛卡尔微分范畴与变化作用模型，并涵盖有限差分与光滑微分。
笛卡尔微分范畴通过微分组合子刻画方向导数，能建模光滑函数微分与微分 λ-演算，但无法容纳有限差分等更离散的微分概念；变化作用模型虽能涵盖这些例子，却过于一般，缺少良好性质。本文引入笛卡尔差分范畴作为二者的桥梁：证明每个笛卡尔微分范畴都是笛卡尔差分范畴，并刻画哪些良行为的变化作用模型可视为笛卡尔差分范畴。该框架同时建模光滑函数的微分演算与有限差分演算。进一步，每个笛卡尔差分范畴都配有切丛单子，其 Kleisli 范畴仍是笛卡尔差分范畴。
Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential categories include classical differential calculus of smooth functions and categorical models of the differential $\lambda$-calculus. However, Cartesian differential categories cannot account for other interesting notions of differentiation of a more discrete nature such as the calculus of finite differences. On the other hand, change action models have been shown to capture these examples as well as more "exotic" examples of differentiation. But change action models are very general and do not share the nice properties of Cartesian differential categories. In this paper, we introduce Cartesian difference categories as a bridge between Cartesian differential categories and change action models. We show that every Cartesian differential category is a Cartesian difference category, and how certain well-behaved change action models are Cartesian difference categories. In particular, Cartesian difference categories model both the differential calculus of smooth functions and the calculus of finite differences. Furthermore, every Cartesian difference category comes equipped with a tangent bundle monad whose Kleisli category is again a Cartesian difference category.