Axiomatic Differential Geometry III-3

TL;DR

This paper explores the connection between classical differential geometry and a modern categorical approach, demonstrating that the embedding preserves Weil functors, thus bridging traditional and contemporary frameworks.

Contribution

It establishes that the canonical embedding from smooth manifolds to functors on Weil algebras preserves Weil functors, linking classical and modern differential geometry.

Findings

Canonical embedding preserves Weil functors

Bridges classical and categorical differential geometry

Enhances understanding of functorial approaches

Abstract

The principal objective in this paer is to study the relationship between the old kingdom of differential geometry (the category of smooth manifolds) and its new kingdom (the category of functors on the category of Weil algebras to some smooth category). It is shown that the canonical embedding of the old kingdom into the new kingdom preserves Weil functors.