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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 Sieve (category theory) ： ウィキペディア英語版 Sieve (category theory) In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection of open subsets of a fixed open set in topology. In a Grothendieck topology, certain sieves become categorical analogues of open covers in topology. ==Definition== Let C be a category, and let ''c'' be an object of C. A sieve ''S'' on ''c'' is a subfunctor of Hom(−, ''c''), i.e., for all objects ''c''′ of C, ''S''(''c''′) ⊆ Hom(''c''′, ''c''), and for all arrows ''f'':''c''″→''c''′, ''S''(''f'') is the restriction of Hom(''f'', ''c''), the pullback by ''f'' (in the sense of precomposition, not of fiber products), to ''S''(''c''′). Put another way, a sieve is a collection ''S'' of arrows with a common codomain which satisfies the functoriality condition, "If ''g'':''c''′→''c'' is an arrow in ''S'', and if ''f'':''c''″→''c''′ is any other arrow in C, then the pullback is in ''S''." Consequently sieves are similar to right ideals in ring theory or filters in order theory. 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「Sieve (category theory)」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.