翻訳と辞書 Words near each other ・ Quittin' Time ・ Quitting ・ Quittner ・ Quittor ・ Quitu culture ・ Quitupan ・ Quitzdorf am See ・ Quitzin Hunting Lodge ・ Quitéria River ・ Quitéro River ・ Quiun Qeshlaqi ・ Quiver ・ Quiver (comics) ・ Quiver (disambiguation) ・ Quiver (KTU album) ・ Quiver (mathematics) ・ Quiver (Monk album) ・ Quiver (video game) ・ Quiver Creek ・ Quiver diagram ・ Quiver Party ・ Quiver River ・ Quiver tip ・ Quiver Township, Mason County, Illinois ・ Quiver Tree Forest ・ Quiverfull ・ Quivet ・ Quivicán ・ Quivicán Municipal Museum ・ Quiviger 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 Quiver (mathematics) ： ウィキペディア英語版 Quiver (mathematics) In mathematics, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph. They are commonly used in representation theory: a representation ''V'' of a quiver assigns a vector space ''V''(''x'') to each vertex ''x'' of the quiver and a linear map ''V''(''a'') to each arrow ''a''. In category theory, a quiver can be understood to be an underlying structure of a category, but without identity morphisms and composition. That is, there is a forgetful functor from Cat to Quiv. Its left adjoint is a free functor which, from a quiver, makes the corresponding free category. ==Definition== A quiver Γ consists of: * The set ''V'' of vertices of Γ * The set ''E'' of edges of Γ * Two functions: ''s'': ''E'' → ''V'' giving the ''start'' or ''source'' of the edge, and another function, ''t'': ''E'' → ''V'' giving the ''target'' of the edge. This definition is identical to that of a multidigraph. A morphism of quivers is defined as follows. If $\backslash Gamma=(V,E,s,t)$ and $\backslash Gamma\text{'}=(V\text{'},E\text{'},s\text{'},t\text{'})$ are two quivers, then a morphism $m=(m\_v,\; m\_e)$ of quivers consist of two functions $m\_v:\; V\backslash to\; V\text{'}$ and $m\_e:\; E\backslash to\; E\text{'}$ such that following diagrams commute: :$m\_v\; \backslash circ\; s\; =\; s\text{'}\; \backslash circ\; m\_e$ and :$m\_v\; \backslash circ\; t\; =\; t\text{'}\; \backslash circ\; m\_e$ 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「Quiver (mathematics)」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.