翻訳と辞書 Words near each other ・ Projective cone ・ Projective connection ・ Projective cover ・ Projective differential geometry ・ Projective frame ・ Projective geometry ・ Projective group (disambiguation) ・ Projective harmonic conjugate ・ Projective hierarchy ・ Projective Hilbert space ・ Projective identification ・ Projective line ・ Projective line over a ring ・ Projective linear group ・ Projective module ・ Projective object ・ Projective orthogonal group ・ Projective plane ・ Projective polyhedron ・ Projective range ・ Projective representation ・ Projective set (disambiguation) ・ Projective Set (game) ・ Projective space ・ Projective superspace ・ Projective test ・ Projective texture mapping ・ Projective unitary group ・ Projective variety ・ Projective vector field 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 Projective object ： ウィキペディア英語版 Projective object In category theory, the notion of a projective object generalizes the notion of a projective module. An object ''P'' in a category C is projective if the hom functor :$\backslash operatorname(P,-)\backslash colon\backslash mathcal\backslash to\backslash mathbf$ preserves epimorphisms. That is, every morphism ''f:P→X'' factors through every epi ''Y→X''. Let $\backslash mathcal$ be an abelian category. In this context, an object $P\backslash in\backslash mathcal$ is called a ''projective object'' if :$\backslash operatorname(P,-)\backslash colon\backslash mathcal\backslash to\backslash mathbf$ is an exact functor, where $\backslash mathbf$ is the category of abelian groups. The dual notion of a projective object is that of an injective object: An object $Q$ in an abelian category $\backslash mathcal$ is ''injective'' if the $\backslash operatorname(-,Q)$ functor from $\backslash mathcal$ to $\backslash mathbf$ is exact. ==Enough projectives== Let $\backslash mathcal$ be an abelian category. $\backslash mathcal$ is said to have enough projectives if, for every object $A$ of $\backslash mathcal$, there is a projective object $P$ of $\backslash mathcal$ and an exact sequence :$P\; \backslash longrightarrow\; A\; \backslash longrightarrow\; 0.$ In other words, the map $p\backslash colon\; P\; \backslash to\; A$ is "epi", or an epimorphism. 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「Projective object」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.