V2EX yoneda lemma

Yoneda Lemma

释义 Definition

Yoneda lemma(米田引理)是范畴论中的一个核心定理:它说明“一个对象由它与所有对象之间的态射所形成的函子(Hom-函子)完全刻画”。直观上,它把“研究对象本身”转化为“研究对象在整个范畴中的关系与作用方式”。

发音 Pronunciation (IPA)

/jned lm/

例句 Examples

The Yoneda lemma is a key tool in category theory.
米田引理是范畴论中的一个关键工具。

Using the Yoneda lemma, we can identify natural transformations from a representable functor with elements of a set associated to the object.
借助米田引理,我们可以把从一个可表函子出发的自然变换与某个与该对象相关的集合元素对应起来。

词源 Etymology

“Yoneda”来自日本数学家米田信夫(Nobuo Yoneda)的姓氏;“lemma”在数学语境中指“引理”,即为证明更重要结论而使用的辅助定理。该引理因其在范畴论中的基础地位而广为人知。

相关词 Related Words

文学与名著作品 Literary Works

  • Categories for the Working Mathematician(Saunders Mac Lane)
  • Category Theory(Steve Awodey)
  • Category Theory in Context(Emily Riehl)
  • Basic Category Theory(Tom Leinster)
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