# Axiomatic Differential Geometry III-1

@article{Nishimura2012AxiomaticDG, title={Axiomatic Differential Geometry III-1}, author={Hirokazu Nishimura}, journal={arXiv: Differential Geometry}, year={2012}, pages={1-12} }

In this paper is proposed a kind of model theory for our axiomatic differential geometry. It is claimed that smooth manifolds, which have occupied the center stage in differential geometry, should be replaced by functors on the category of Weil algebras. Our model theory is geometrically natural and conceptually motivated, while the model theory of synthetic differential geometry is highly artificial and exquisitely technical.

## 5 Citations

Axiomatic Differential Geometry ?-1

- Mathematics
- 2012

In this paper is proposed a kind of model theory for our axiomatic differential geometry. It is claimed that smooth manifolds, which have occupied the center stage in differential geometry, should be…

Axiomatic Differential Geometry III-3-Its Landscape-Chapter 3: The Old Kingdom of Differential Geometers

- Mathematics
- 2012

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…

Weil Diffeology I: Classical Differential Geometry

- Mathematics
- 2017

Topos theory is a category-theoretic axiomatization of set theory. Model categories are a category-theoretical framework for abstract homotopy theory. They are complete and cocomplete categories…

Differential Structure, Tangent Structure, and SDG

- MathematicsAppl. Categorical Struct.
- 2014

It is shown that tangent structures appropriately span a very wide range of definitions, from the syntactic and structural differentials arising in computer science and combinatorics, through the concrete manifolds of algebraic and differential geometry, and finally to the abstract definitions of synthetic differential geometry.

AXIOMATIC DIFFERENTIAL GEOMETRY II-3 - ITS DEVELOPMENTS - CHAPTER 3: THE GENERAL JACOBI IDENTITY

- Mathematics
- 2013

As the fourth paper of our series of papers concerned with ax- iomatic differential geometry, this paper is devoted to the general Jacobi iden- tity supporting the Jacobi identity of vector fields.…

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