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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 Full and faithful functors ： ウィキペディア英語版 Full and faithful functors In category theory, a faithful functor (resp. a full functor) is a functor that is injective (resp. surjective) when restricted to each set of morphisms that have a given source and target. ==Formal definitions== Explicitly, let ''C'' and ''D'' be (locally small) categories and let ''F'' : ''C'' → ''D'' be a functor from ''C'' to ''D''. The functor ''F'' induces a function :$F\_\backslash colon\backslash mathrm\_(X,Y)\backslash rightarrow\backslash mathrm\_(F(X),F(Y))$ for every pair of objects ''X'' and ''Y'' in ''C''. The functor ''F'' is said to be *faithful if ''F''''X'',''Y'' is injective〔Mac Lane (1971), p. 15〕〔Jacobson (2009), p. 22〕 *full if ''F''''X'',''Y'' is surjective〔〔Mac Lane (1971), p. 14〕 *fully faithful if ''F''''X'',''Y'' is bijective for each ''X'' and ''Y'' in ''C''. 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「Full and faithful functors」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.