论文标题
差分微积分的功能方法
A functorial approach to differential calculus
论文作者
论文摘要
我们表明，差分演算（以其通常形式或以拓扑差分结石的一般形式）可以完全分解为函子类别（来自小类锚固切线代数到锚定集的函数）。为了准备这种方法，我们定义了一种新的，对称的差分演示，其主要特征是锚图播放的中央r {prot {fly {f。我们详细研究。我们开发该理论的目的是双重的：（1）在任何交换环（包括有限环）上定义微积分的设置； （2）定义一个可以推广到分级环（超差分计算）的设置。
We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets). To prepare this approach, we define a new, symmetric, presentation of differential calculus, whose main feature is the central r{ô}le played by the anchor map, which we study in detail. Our aim for developing this theory is twofold: (1) define a setting for calculus over any commutative ring, including finite rings; (2) define a setting that can be generalized to categories of graded rings (super differential calculus).
