A functorial approach to differential calculus
Algebraic Geometry
2021-03-25 v2 Category Theory
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).
Cite
@article{arxiv.2006.04452,
title = {A functorial approach to differential calculus},
author = {Wolfgang Bertram and Jérémy Haut},
journal= {arXiv preprint arXiv:2006.04452},
year = {2021}
}