翻訳と辞書 Words near each other ・ Location-scale family ・ Locational astrology ・ Locationes mansorum desertorum ・ LocationFree Player ・ Locationized firearm ・ Locationized gun ・ Locations associated with Arthurian legend ・ Locations in Australia with an English name ・ Locations in Canada with an English name ・ Locations in His Dark Materials ・ Locations in Jericho (TV series) ・ Locations in the Bionicle Saga ・ Localizer ・ Localizer performance with vertical guidance ・ Localizer type directional aid ・ Localizing subcategory ・ LocalLabs ・ Locallife ・ Locally acyclic morphism ・ Locally catenative sequence ・ Locally compact field ・ Locally compact group ・ Locally compact quantum group ・ Locally compact space ・ Locally connected space ・ Locally constant function ・ Locally convex topological vector space ・ Locally cyclic group ・ Locally decodable code ・ Locally discrete collection 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 Localizing subcategory ： ウィキペディア英語版 Localizing subcategory In mathematics, Serre and localizing subcategories form important classes of subcategories of an abelian category. Localizing subcategories are certain Serre subcategories. They are strongly linked to the notion of a quotient category. == Serre subcategories == Let $\backslash mathcal$ be an abelian category. A non-empty full subcategory $\backslash mathcal$ is called a ''Serre subcategory'' (or also a ''dense subcategory''), if for every short exact sequence $0\backslash rightarrow$ A' \rightarrow A\rightarrow A''\rightarrow 0 in $\backslash mathcal$ the object $A$ is in $\backslash mathcal$ if and only if the objects $A\text{'}$ and $A\text{'}\text{'}$ belong to $\backslash mathcal$. In words: $\backslash mathcal$ is closed under subobjects, quotient objects and extensions. The importance of this notion stems from the fact that kernels of exact functors between abelian categories have this property, and that one can build (for locally small $\backslash mathcal$) the quotient category (in the sense of Gabriel, Grothendieck, Serre) $\backslash mathcal/\backslash mathcal$, which has the same objects as $\backslash mathcal$, is abelian, and comes with an exact functor (called the quotient functor) $T\backslash colon\backslash mathcal\backslash rightarrow\backslash mathcal/\backslash mathcal$ whose kernel is $\backslash mathcal$. 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「Localizing subcategory」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.