翻訳と辞書 Words near each other ・ Inverse electron-demand Diels–Alder reaction ・ Inverse element ・ Inverse exchange-traded fund ・ Inverse Faraday effect ・ Inverse filter ・ Inverse filter (disambiguation) ・ Inverse floating rate note ・ Inverse function ・ Inverse function theorem ・ Inverse functions and differentiation ・ Inverse Galois problem ・ Inverse gambler's fallacy ・ Inverse gas chromatography ・ Inverse Gaussian distribution ・ Inverse hyperbolic function ・ Inverse image functor ・ Inverse iteration ・ Inverse kinematics ・ Inverse Laplace transform ・ Inverse limit ・ Inverse magnetostrictive effect ・ Inverse mapping theorem ・ Inverse matrix gamma distribution ・ Inverse mean curvature flow ・ Inverse method ・ Inverse Mills ratio ・ Inverse multiplexer ・ Inverse Multiplexing for ATM ・ Inverse number ・ Inverse parser Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Inverse image functor ： ウィキペディア英語版 Inverse image functor In mathematics, the inverse image functor is a covariant construction of sheaves. The direct image functor is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle features. ==Definition== Suppose given a sheaf $\backslash mathcal$ on $Y$ and that we want to transport $\backslash mathcal$ to $X$ using a continuous map $f\backslash colon\; X\backslash to\; Y$. We will call the result the ''inverse image'' or pullback sheaf $f^\backslash mathcal$. If we try to imitate the direct image by setting :$f^\backslash mathcal(U)\; =\; \backslash mathcal(f(U))$ for each open set $U$ of $X$, we immediately run into a problem: $f(U)$ is not necessarily open. The best we could do is to approximate it by open sets, and even then we will get a presheaf and not a sheaf. Consequently, we define $f^\backslash mathcal$ to be the sheaf associated to the presheaf: :$U\; \backslash mapsto\; \backslash varinjlim\_\backslash mathcal(V).$ (Here $U$ is an open subset of $X$ and the colimit runs over all open subsets $V$ of $Y$ containing $f(U)$.) For example, if $f$ is just the inclusion of a point $y$ of $Y$, then $f^(\backslash mathcal)$ is just the stalk of $\backslash mathcal$ at this point. The restriction maps, as well as the functoriality of the inverse image follows from the universal property of direct limits. When dealing with morphisms $f\backslash colon\; X\backslash to\; Y$ of locally ringed spaces, for example schemes in algebraic geometry, one often works with sheaves of $\backslash mathcal\_Y$-modules, where $\backslash mathcal\_Y$ is the structure sheaf of $Y$. Then the functor $f^$ is inappropriate, because in general it does not even give sheaves of $\backslash mathcal\_X$-modules. In order to remedy this, one defines in this situation for a sheaf of $\backslash mathcal\; O\_Y$-modules $\backslash mathcal\; G$ its inverse image by :$f^$ *\mathcal G := f^\mathcal \otimes__Y} \mathcal_X. 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「Inverse image functor」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.