Axiomatic differential geometry. III-2 -- its landscape. II: Model theory. II (Q2844352)
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scientific article; zbMATH DE number 6202492
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Axiomatic differential geometry. III-2 -- its landscape. II: Model theory. II |
scientific article; zbMATH DE number 6202492 |
Statements
28 August 2013
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axiomatic differential geometry
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synthetic differential geometry
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DG-category
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Cartesian closed
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locally Cartesian closed
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math.DG
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Axiomatic differential geometry. III-2 -- its landscape. II: Model theory. II (English)
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Given a complete and (locally) Cartesian closed category \(\mathbf{U}\), it is shown that the category of functors from the category of Weil algebras to the category \(\mathbf{U}\) is (locally, respectively) Cartesian closed. The corresponding axiomatization for differential geometry based upon Weil functors and formulated by the author in a previous article [ibid. 74, No. 1, 17--26 (2013; Zbl 1281.51014)], is then given.
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