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Axiomatic Differential Geometry III-3-Its Landscape-Chapter 3: The Old Kingdom of Differential Geometers
Institute of Mathematics University of Tsukuba, Tsukuba, Japan
- 1 Institute of Mathematics University of Tsukuba, Tsukuba, Japan
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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.
KeywordsAxiomatic Differential GeometrySynthetic DifferentialGeometryWeil AlgebraWeil Functor
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