faithful functor

忠实函子

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

Translation evidence: Literature usage

Meaning in context

A functor inducing an injective map on each hom-set for a fixed pair of source objects.

对来源范畴任意一对对象，诱导的态射集映射均为单射的函子。

Example

The forgetful functor Vectk→Set\mathbf{Vect}_k\to\mathbf{Set} is faithful.

Usage and distinctions

Faithfulness need not distinguish objects; it distinguishes parallel morphisms.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.5, Definition 1.5.7 · 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」，紧随 def:functor 的定义，项「忠实」 · Checked 2026-10-14
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