一句话：在笛卡尔微分范畴中用函子与单子刻画泰勒展开，统一高阶导数、对偶数与 jet bundle。
本文在笛卡尔微分范畴的框架下提出一种组合式的泰勒展开理论。核心思想是把泰勒展开刻画为一个函子，该函子将通常的切丛函子推广到高阶导数情形。泰勒展开的基本性质被归结为自然性方程，这些方程使该函子成为一个单子。借助这一单子结构，作者给出了高阶对偶数以及自动微分中 jet bundle 构造的范畴论解释。论文属于范畴论与形式语义的基础工作，主要结果是对泰勒展开的组合性与单子性质的刻画，并说明其可统一高阶导数和相关微分构造；评估以数学定义与性质证明为主，不涉及实现或实验。
This paper provides a compositional approach to Taylor expansion, in the setting of cartesian differential categories. Taylor expansion is captured here by a functor that generalizes the tangent bundle functor to higher order derivatives. The fundamental properties of Taylor expansion then boils down to naturality equations that turns this functor into a monad. This monad provides a categorical approach to higher order dual numbers and the jet bundle construction used in automated differentiation.