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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Global section functor ： ウィキペディア英語版 Global section functor Let ''X'' be a topological space, and $\backslash mathrm\; (X,\; \backslash mathcal\; C)$ denote the category of sheaves with values in $\backslash mathcal\; C$. Then the map that associates to a sheaf $\backslash mathcal\; F$ its global sections $\backslash Gamma(X,\backslash mathcal\; F)$ is a covariant functor to $\backslash mathcal\; C$. If $\backslash mathcal\; C$ is the category of abelian groups, then this functor is left exact. This important remark leads to the notion of sheaf cohomology, ''via'' derived functors. ==Examples== *Let $\}\_X)\; =\; \backslash mathbb\; Z^$, i.e. the direct sum indexed by connected components of ''X'' *Let $\backslash mathcal\; O\_X$ be the sheaf of holomorphic functions on the compact connected complex manifold ''X'', then by the maximum principle, global sections are constant, ''ie.'' $\backslash Gamma\; (X,\; \backslash mathcal\; O\_X)\; =\; \backslash mathbb\; C$ *Let $\backslash mathcal\; O\; (i),\; i\backslash in\; \backslash mathbb\; Z$ denote the twisting sheaves on the projective space $\backslash mathbb\; P\_k^n$, then $\backslash Gamma\; (X,\; \backslash mathcal\; O(d))\; =\; k\_d(\backslash ldots,\; X\_n)$ for $d\; \backslash ge\; 0$, and 0 for . 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「Global section 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.