V2EX functorial

Functorial

释义 Definition

(数学范畴论)函子性的;函子相关的。
指某个构造、对应或过程能够以“函子(functor)”的方式进行:不仅把对象对应到对象,还能把态射(映射)对应到态射,并且保持复合与恒等等结构性质。(该词也常更宽泛地表示“以自然、结构保持的方式随映射变化”。)

例句 Examples

A functorial construction works the same way for every map.
函子性的构造对每一个映射都以相同的方式起作用。

The long exact sequence in homology is functorial: a continuous map between spaces induces compatible maps between their homology groups, preserving composition.
同调中的长正合序列是函子性的:空间之间的连续映射会诱导出它们同调群之间相容的映射,并保持复合关系。

发音 Pronunciation (IPA)

/fktril/

词源 Etymology

functorial 来自 functor(函子) + 形容词后缀 -ial(表示“……的”)。
functor 源于拉丁语 functor,与 fungi(“执行、履行”)有关;在现代数学中,“函子”被用来表示在不同范畴之间“执行/实现”结构对应的规则,因此 functorial 就表示“符合函子方式的、结构保持的”。

相关词 Related Words

文学与经典作品 Literary & Notable Works

  • Categories for the Working Mathematician(Saunders Mac Lane)
  • Category Theory(Steve Awodey)
  • Basic Category Theory(Tom Leinster)
  • Homology(Saunders Mac Lane)
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