Differential Geometry in Toposes
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Solution of the vacuum Einstein equations in Synthetic Differential Geometry of Kock-Lawvere
The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. It is known that topos-theoretic geometry can be successfully developed within the framework of Synthetic Differential Geometry of Kock-Lawvere (SDG), the models of which are serving the toposes, i.e. categories possessing many characteristics of traditional The...
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Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the computationally dense ones) are seen to be the ones whose ‘lifts’ to a kind of completion have right adjoints. We characterize topos inclusions corresponding to a general form of relative computability. We characterize p...
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متن کاملExact completions and toposes
Toposes and quasi-toposes have been shown to be useful in mathematics, logic and computer science. Because of this, it is important to understand the different ways in which they can be constructed. Realizability toposes and presheaf toposes are two important classes of toposes. All of the former and many of the latter arise by adding “good” quotients of equivalence relations to a simple catego...
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From Hilbert’s theorem of zeroes, and from Noether’s ideal theory, Birkhoff [1] derived certain algebraic concepts (as explained by Tholen [10]) that have a dual significance in general toposes, similar to their role in the original examples of algebraic geometry. I will describe a simple example that illustrates some of the aspects of this relationship. The dualization from algebra to geometry...
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تاریخ انتشار 2009