Axiomatic Differential Geometry III-1

zbMATH Open1281.51014arXiv1209.1247MaRDI QIDQ2844343

Hirozaku Nishimura

Publication date: 28 August 2013

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1209.1247

zbMATH Keywords

Weil algebraWeil functoraxiomatic differential geometryconvenient category of smooth spaces

Mathematics Subject Classification ID

Distance geometry (51K99) Categories in geometry and topology (18F99) Synthetic differential geometry (51K10) Topos-theoretic approach to differentiable manifolds (58A03)

Recommendations

• Unnamed Item 👍 👎
• Unnamed Item 👍 👎
• Geometrical axiomatization for model complete theories of differential topological fields 👍 👎
• Some models in differential geometry 👍 👎
• Geometric models of twisted differential \(K\)-theory. I 👍 👎
• Axiomatic Differential Geometry III-2 👍 👎
• Axiomatic Differential Geometry I-1 👍 👎
• Axiomatic Differential Geometry II-1 Vector Fields 👍 👎
• Aspects of Differential Geometry III 👍 👎
• Axiomatic differential geometry II-2 - differential forms 👍 👎

This page was built for publication: Axiomatic Differential Geometry III-1