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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 Direct image functor ： ウィキペディア英語版 Direct image functor In mathematics, in the field of sheaf theory and especially in algebraic geometry, the direct image functor generalizes the notion of a section of a sheaf to the relative case. ==Definition== Let ''f'': ''X'' → ''Y'' be a continuous mapping of topological spaces, and ''Sh''(–) the category of sheaves of abelian groups on a topological space. The direct image functor :$f\_$ *: Sh(X) \to Sh(Y) sends a sheaf ''F'' on ''X'' to its direct image presheaf :$f\_$ *F(U) := F(f^(U)), which turns out be a sheaf on ''Y''. This assignment is functorial, i.e. a morphism of sheaves φ: ''F'' → ''G'' on ''X'' gives rise to a morphism of sheaves ''f''∗(φ): ''f''∗(''F'') → ''f''∗(''G'') on ''Y''. 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「Direct 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.