natural transformation

自然变换

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

Translation evidence: Literature usage

Meaning in context

For $F,G:C\to D$, components $\eta_X:F(X)\to G(X)$ satisfying $G(f)\eta_X=\eta_YF(f)$ for every $f:X\to Y$.

对于 F、G:C→D，由分量 η_X:F(X)→G(X) 组成且对每个 f:X→Y 满足 G(f)η_X=η_YF(f) 的族。

Example

The projections $A\times A\to A$ are natural in $A$.

Usage and distinctions

A collection of correctly typed components need not satisfy naturality.

Read the encyclopedia explanation

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Definition sources

1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.4, Definition 1.4.1 · 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」，定义「自然变换，或函子间的态射」 · Checked 2026-10-14

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