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- Synthetic_differential_geometry abstract "In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory. There are several insights that allow for such a reformulation. The first is that most of the analytic data for describing the class of smooth manifolds can be encoded into certain fibre bundles on manifolds: namely bundles of jets (see also jet bundle). The second insight is that the operation of assigning a bundle of jets to a smooth manifold is functorial in nature. The third insight is that over a certain category, these are representable functors. Furthermore, their representatives are related to the algebras of dual numbers, so that smooth infinitesimal analysis may be used.Synthetic differential geometry can serve as a platform for formulating certain otherwise obscure or confusing notions from differential geometry. For example, the meaning of what it means to be natural (or invariant) has a particularly simple expression, even though the formulation in classical differential geometry may be quite difficult.".
- Synthetic_differential_geometry wikiPageExternalLink download?doi=10.1.1.114.1930&rep=rep1&type=pdf.
- Synthetic_differential_geometry wikiPageExternalLink sdg99.pdf.
- Synthetic_differential_geometry wikiPageExternalLink SDG_Outline.pdf.
- Synthetic_differential_geometry wikiPageExternalLink sdg.pdf.
- Synthetic_differential_geometry wikiPageExternalLink pizza-seminar.pdf.
- Synthetic_differential_geometry wikiPageID "3869427".
- Synthetic_differential_geometry wikiPageLength "2138".
- Synthetic_differential_geometry wikiPageOutDegree "16".
- Synthetic_differential_geometry wikiPageRevisionID "681262938".
- Synthetic_differential_geometry wikiPageWikiLink Category:Differential_geometry.
- Synthetic_differential_geometry wikiPageWikiLink Category_theory.
- Synthetic_differential_geometry wikiPageWikiLink Differentiable_manifold.
- Synthetic_differential_geometry wikiPageWikiLink Differential_geometry.
- Synthetic_differential_geometry wikiPageWikiLink Dual_number.
- Synthetic_differential_geometry wikiPageWikiLink Dual_numbers.
- Synthetic_differential_geometry wikiPageWikiLink Fiber_bundle.
- Synthetic_differential_geometry wikiPageWikiLink Fibre_bundle.
- Synthetic_differential_geometry wikiPageWikiLink Functor.
- Synthetic_differential_geometry wikiPageWikiLink Jet_(mathematics).
- Synthetic_differential_geometry wikiPageWikiLink Jet_bundle.
- Synthetic_differential_geometry wikiPageWikiLink John_Lane_Bell.
- Synthetic_differential_geometry wikiPageWikiLink Mathematics.
- Synthetic_differential_geometry wikiPageWikiLink Michael_Shulman_(mathematician).
- Synthetic_differential_geometry wikiPageWikiLink Representable_functor.
- Synthetic_differential_geometry wikiPageWikiLink Smooth_infinitesimal_analysis.
- Synthetic_differential_geometry wikiPageWikiLink Smooth_manifold.
- Synthetic_differential_geometry wikiPageWikiLink Topos.
- Synthetic_differential_geometry wikiPageWikiLink Topos_theory.
- Synthetic_differential_geometry wikiPageWikiLink William_Lawvere.
- Synthetic_differential_geometry wikiPageWikiLinkText "Synthetic differential geometry".
- Synthetic_differential_geometry wikiPageWikiLinkText "synthetic differential geometry".
- Synthetic_differential_geometry hasPhotoCollection Synthetic_differential_geometry.
- Synthetic_differential_geometry wikiPageUsesTemplate Template:Infinitesimals.
- Synthetic_differential_geometry wikiPageUsesTemplate Template:Inline.
- Synthetic_differential_geometry subject Category:Differential_geometry.
- Synthetic_differential_geometry hypernym Formalization.
- Synthetic_differential_geometry type Article.
- Synthetic_differential_geometry type Scientist.
- Synthetic_differential_geometry type Article.
- Synthetic_differential_geometry type Field.
- Synthetic_differential_geometry type Physic.
- Synthetic_differential_geometry comment "In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory. There are several insights that allow for such a reformulation. The first is that most of the analytic data for describing the class of smooth manifolds can be encoded into certain fibre bundles on manifolds: namely bundles of jets (see also jet bundle).".
- Synthetic_differential_geometry label "Synthetic differential geometry".
- Synthetic_differential_geometry sameAs m.0b4672.
- Synthetic_differential_geometry sameAs Sentetik_diferansiyel_geometri.
- Synthetic_differential_geometry sameAs Q7662747.
- Synthetic_differential_geometry sameAs Q7662747.
- Synthetic_differential_geometry wasDerivedFrom Synthetic_differential_geometry?oldid=681262938.
- Synthetic_differential_geometry isPrimaryTopicOf Synthetic_differential_geometry.