翻訳と辞書
Words near each other
・ "O" Is for Outlaw
・ "O"-Jung.Ban.Hap.
・ "Ode-to-Napoleon" hexachord
・ "Oh Yeah!" Live
・ "Our Contemporary" regional art exhibition (Leningrad, 1975)
・ "P" Is for Peril
・ "Pimpernel" Smith
・ "Polish death camp" controversy
・ "Pro knigi" ("About books")
・ "Prosopa" Greek Television Awards
・ "Pussy Cats" Starring the Walkmen
・ "Q" Is for Quarry
・ "R" Is for Ricochet
・ "R" The King (2016 film)
・ "Rags" Ragland
・ ! (album)
・ ! (disambiguation)
・ !!
・ !!!
・ !!! (album)
・ !!Destroy-Oh-Boy!!
・ !Action Pact!
・ !Arriba! La Pachanga
・ !Hero
・ !Hero (album)
・ !Kung language
・ !Oka Tokat
・ !PAUS3
・ !T.O.O.H.!
・ !Women Art Revolution


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

synthetic differential geometry : ウィキペディア英語版
synthetic differential geometry

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.
== Further reading ==

*John Lane Bell, (Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets ) (PDF file)
*F.W. Lawvere, (Outline of synthetic differential geometry ) (PDF file)
*Anders Kock, (Synthetic Differential Geometry ) (PDF file), Cambridge University Press, 2nd Edition, 2006.
*R. Lavendhomme, ''Basic Concepts of Synthetic Differential Geometry'', Springer-Verlag, 1996.
*Michael Shulman, (Synthetic Differential Geometry )
*Ryszard Paweł Kostecki, (Differential Geometry in Toposes )

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「synthetic differential geometry」の詳細全文を読む



スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース

Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.