V2EX morphisms

Morphisms

Definition / 定义

morphism(复数:morphisms):在数学(尤其是范畴论、代数、几何)中指一种“保持结构的映射/箭头”,用来表示两个对象之间允许的关系或变换(例如函数、线性映射、群同态等都可视为不同范畴中的 morphism)。在具体语境里,它常与 object(对象) 一起出现。
(注:在不同数学分支中,morphism 的具体含义会随“范畴”的定义而变化。)

Pronunciation / 发音(IPA)

/mr.f.zmz/

Examples / 例句

In this category, morphisms are just ordinary functions.
在这个范畴里,态射就是普通的函数。

Composing morphisms lets us track how structure-preserving maps interact across several steps.
通过复合态射,我们可以追踪多个步骤中保持结构的映射如何相互作用。

Etymology / 词源

来自 **morph-**(表示“形状、形式”,源自希腊语 morphē “形态”)+ -ism(名词后缀,表示“体系/概念/性质”)。在现代数学语境中,morphism 被用来强调“从一个对象到另一个对象的形式/结构上的变换”,复数为 morphisms

Related Words / 相关词

Literary Works / 文献与著作中的用例

  • Categories for the Working Mathematician(Saunders Mac Lane):系统使用 “morphisms” 作为范畴论核心术语。
  • Basic Category Theory(Tom Leinster):入门教材中频繁出现 “objects and morphisms”。
  • Sheaves in Geometry and Logic(Mac Lane & Moerdijk):在层与逻辑的框架下大量讨论各类 morphisms。
  • Algebra(Serge Lang):在代数结构讨论中常以同态等作为典型 morphisms 出现。
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