2012/09/06 by Hirokazu Nishimura, Nishimura, Hirokazu
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #math.DG
paper · pdf · doi:10.48550/arxiv.1209.1247
openalex publication_date 2012/09/06 · arxiv created 2012/09/27 · arxiv updated 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.