full functor

全函子

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

Translation evidence: Literature usage

Meaning in context

A functor inducing a surjective 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满射的函子。

Example

The inclusion of abelian groups into groups is full.

Usage and distinctions

Fullness is about arrows between image objects, not about reaching every target object.

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「全」 · Checked 2026-10-14
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