TITLE:
Axiomatic Differential Geometry III-3-Its Landscape-Chapter 3: The Old Kingdom of Differential Geometers
AUTHORS:
Hirokazu Nishimura
KEYWORDS:
Axiomatic Differential Geometry, Synthetic Differential, Geometry, Weil Algebra, Weil Functor
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.6,
June
21,
2017
ABSTRACT: 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.