V2EX derived category

Derived Category

释义 Definition

导出范畴:同调代数与代数几何中的一个基本概念。它把“链复形”按“拟同构(quasi-isomorphism)等价”进行系统化处理,从而在一个更合适的范畴里研究同调信息、导出函子、扩张(Ext)等对象。

发音 Pronunciation (IPA)

/dravd ktri/

例句 Examples

The derived category helps us compare complexes up to quasi-isomorphism.
导出范畴帮助我们在拟同构意义下比较链复形。

In algebraic geometry, many cohomological constructions are most naturally expressed in the derived category of sheaves.
在代数几何中,许多上同调相关的构造用层的导出范畴来表达最为自然。

词源 Etymology

derived 源自拉丁语 derivare(“引出、派生”),在数学里常表示“由某个基础对象通过系统过程得到的”。category 来自希腊语 kategoria(“归类、范畴”)。合起来,derived category 指“通过导出(派生)过程得到、用于组织与比较同调信息的范畴”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Categories and Sheaves(Saunders Mac Lane & Ieke Moerdijk)
  • Sheaves in Geometry and Logic(Saunders Mac Lane & Ieke Moerdijk)
  • Residues and Duality(Robin Hartshorne;以 Grothendieck 的思想为背景,常涉及导出范畴语言)
  • Methods of Homological Algebra(Sergei I. Gelfand & Yuri I. Manin)
  • An Introduction to Homological Algebra(Charles A. Weibel)
  • Séminaire Bourbaki 与 Verdier 等人关于 catégorie dérivée / derived category 的经典讲义与论文(导出范畴的早期系统化来源)
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