V2EX abelian category

Abelian Category

释义 Definition

Abelian category(阿贝尔范畴)是范畴论与同调代数中的一种“像阿贝尔群那样好用”的范畴:它是加法范畴,并且对任意态射都存在核(kernel)与余核(cokernel),所有单态射与满态射都分别是某个核/余核,因而可以在其中自然地讨论短正合列、同调等结构。常见例子包括阿贝尔群的范畴、模的范畴、(适当条件下的)层的范畴等。

发音 Pronunciation (IPA)

/bilin ktri/

例句 Examples

An abelian category has kernels and cokernels.
阿贝尔范畴具有核与余核。

Many arguments in homological algebra become cleaner when working inside an abelian category, where exact sequences behave well.
在同调代数中,许多论证在阿贝尔范畴内会更清晰,因为其中正合列的性质表现良好。

词源 Etymology

Abelian来自挪威数学家尼尔斯亨里克阿贝尔(Niels Henrik Abel)的姓氏,数学中常用来表示“交换的”(如阿贝尔群)。Category源自希腊语 katēgoria(“分类/范畴”之意),在现代数学中被用来指由对象与态射组成的抽象构。“Abelian category”因此可理解为“具有交换性与加法结构、并能良好处理正合性的一类范畴”。

相关词 Related Words

文学与名著中的用例 Literary Works

  • Saunders Mac Lane, Categories for the Working Mathematician(《为工作数学家准备的范畴论》):介绍范畴论基础并讨论阿贝尔范畴相关结构。
  • Peter Freyd, Abelian Categories: An Introduction to the Theory of Functors(《阿贝尔范畴》):专门系统阐述阿贝尔范畴与函子理论。
  • Henri Cartan & Samuel Eilenberg, Homological Algebra(《同调代数》):同调代数经典著作,广泛使用阿贝尔范畴语言。
  • Sergei I. Gelfand & Yuri I. Manin, Methods of Homological Algebra(《同调代数方法》):以阿贝尔范畴与导出范畴为核心工具展开。
  • Saunders Mac Lane & Ieke Moerdijk, Sheaves in Geometry and Logic(《几何与逻辑中的层》):在层论与拓扑斯背景下频繁涉及阿贝尔范畴的例子与应用。
About     Help     Advertise     Blog     API     FAQ     Solana     3737 Online   Highest 6679       Select Language
创意工作者们的社区
World is powered by solitude
VERSION: 3.9.8.5 70ms UTC 04:33 PVG 12:33 LAX 21:33 JFK 00:33
Do have faith in what you're doing.
ubao msn snddm index pchome yahoo rakuten mypaper meadowduck bidyahoo youbao zxmzxm asda bnvcg cvbfg dfscv mmhjk xxddc yybgb zznbn ccubao uaitu acv GXCV ET GDG YH FG BCVB FJFH CBRE CBC GDG ET54 WRWR RWER WREW WRWER RWER SDG EW SF DSFSF fbbs ubao fhd dfg ewr dg df ewwr ewwr et ruyut utut dfg fgd gdfgt etg dfgt dfgd ert4 gd fgg wr 235 wer3 we vsdf sdf gdf ert xcv sdf rwer hfd dfg cvb rwf afb dfh jgh bmn lgh rty gfds cxv xcv xcs vdas fdf fgd cv sdf tert sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf shasha9178 shasha9178 shasha9178 shasha9178 shasha9178 liflif2 liflif2 liflif2 liflif2 liflif2 liblib3 liblib3 liblib3 liblib3 liblib3 zhazha444 zhazha444 zhazha444 zhazha444 zhazha444 dende5 dende denden denden2 denden21 fenfen9 fenf619 fen619 fenfe9 fe619 sdf sdf sdf sdf sdf zhazh90 zhazh0 zhaa50 zha90 zh590 zho zhoz zhozh zhozho zhozho2 lislis lls95 lili95 lils5 liss9 sdf0ty987 sdft876 sdft9876 sdf09876 sd0t9876 sdf0ty98 sdf0976 sdf0ty986 sdf0ty96 sdf0t76 sdf0876 df0ty98 sf0t876 sd0ty76 sdy76 sdf76 sdf0t76 sdf0ty9 sdf0ty98 sdf0ty987 sdf0ty98 sdf6676 sdf876 sd876 sd876 sdf6 sdf6 sdf9876 sdf0t sdf06 sdf0ty9776 sdf0ty9776 sdf0ty76 sdf8876 sdf0t sd6 sdf06 s688876 sd688 sdf86