Topos theory and synthetic differential geometry

The most basic axioms of synthetic differential geometry is not compatible with classical set theory so that they must be interpreted in a more general category [1]. Moerdijk and Reyes has constructed a topos ℰ (i.e. a category with an internal logic) that contains the category of smooth manifolds [...

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Bibliographic Details
Main Author: Afgani, Rizal
Format: Conference Proceeding
Language:English
Subjects:
Axioms
Differential geometry
Semantics
Set theory
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Summary:The most basic axioms of synthetic differential geometry is not compatible with classical set theory so that they must be interpreted in a more general category [1]. Moerdijk and Reyes has constructed a topos ℰ (i.e. a category with an internal logic) that contains the category of smooth manifolds [2] and satisfies the axioms of synthetic differential geometry interpreted via sheaf semantics. In this article we review sheaf semantics of topos and some applications in synthetic differential geometry. In particular, we discuss the R-module structure in ℰ /M of the tangent bundle π : TM → M of a manifold M.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0192007