Cartesian Difference Categories

Cartesian differential categories are equipped with a combinator which axiomatizes the directional derivative. Important models of include classical calculus smooth functions and categorical $\lambda$-calculus. However, cannot account for other interesting notions differentiation more discrete nature such as finite differences. On hand, change action have been shown to capture these examples well "exotic" differentiation. But very general do not share nice properties categories. In this paper, we introduce difference bridge between models. We show that every category is category, how certain well-behaved particular, model both Furthermore, comes tangent bundle monad whose Kleisli again category.