Author(s)

Hirokazu Nishimura

Institute of Mathematics University of Tsukuba, Tsukuba, Japan.

The principal objective of this paper 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.

Axiomatic Differential Geometry, Synthetic Differential, Geometry, Weil Algebra, Weil Functor

Nishimura, H. (2017) Axiomatic Differential Geometry III-3-Its Landscape-Chapter 3: The Old Kingdom of Differential Geometers. Applied Mathematics, 8, 835-845. doi: 10.4236/am.2017.86065.