V2EX coimage

Coimage

定义 Definition

coimage(数学):在范畴论/代数中,一个映射(态射)\(f\) 的 coimage 通常指 \(\mathrm{coker}(\ker f)\)(“核的余核”)。直观上,它把所有必然被映射为零的部分先“压掉”,再得到一个与“像(image)”密切相关的对象;在阿贝尔范畴中,coimage 与 image 常常同构
(该词在日常英语中很少使用,主要见于数学语境。)

发音 Pronunciation

/komd/

例句 Examples

In this proof, we consider the coimage of the map.
在这个证明中,我们考虑该映射的 coimage(余像)。

In an abelian category, the canonical morphism from the coimage to the image is an isomorphism, which helps factor the map in a standard way.
在阿贝尔范畴中,从 coimage(余像)到 image(像)的典范态射是同构,这有助于用标准方式分解该映射。

词源 Etymology

由前缀 co-(表示“对应的、对偶的”或“共同的”概念)+ image(像;源自拉丁语 imago “形象、影像”)构成。在数学里,co- 常用来标记与某个概念“对偶/余”方向相关的对象(如 cokernel 余),因此 coimage 常译为“余像”。

相关词 Related Words

文学与名著用例 Literary Works

  • Categories for the Working Mathematician(Saunders Mac Lane):在讨论像/余像、核/余核等概念时会使用 coimage
  • An Introduction to Homological Algebra(Charles A. Weibel):在同调代数与阿贝尔范畴的语境中出现 coimage
  • Basic Category Theory(Tom Leinster):涉及阿贝尔范畴或相关补充材料时可能出现 coimage(视版本与章节而定)。
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