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arXiv · 2006.04452

A functorial approach to differential calculus

Wolfgang Bertram·Jérémy Haut
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Abstract

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{\^o}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).

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Wolfgang Bertram, Jérémy Haut. 2020-06-08. A functorial approach to differential calculus. https://arxiv.org/abs/2006.04452

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