natural isomorphism

自然同构

Category Theory · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A natural transformation all of whose components are isomorphisms, equivalently an invertible morphism in the functor category.

各分量均为同构的自然变换；等价地，是函子范畴中的可逆态射。

Example

(a,b)↦(b,a)(a,b)\mapsto(b,a) naturally identifies A×BA\times B and B×AB\times A.

Usage and distinctions

Pointwise existence of unrelated isomorphisms does not guarantee a natural isomorphism.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.4, Exercise 1.4.i; §1.5, discussion preceding Definition 1.5.4 · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法，第一卷（作者源码）第2章，「函子与自然变换」，约定 con:naturaltrans-morphism 中「自然同构」及范畴等价讨论 · Checked 2026-10-14
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