locally small category

局部小范畴

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

Translation evidence: Literature usage

Meaning in context

A category whose collection of morphisms between each fixed pair of objects is a set.

任意固定的一对对象之间的态射构成集合的范畴。

Example

Set\mathbf{Set} is locally small although the class of all sets is not a set.

Usage and distinctions

The Chinese source explicitly uses 局部 U-小范畴; this entry suppresses the fixed universe, as its convention allows.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.1, Definition 1.1.7 · 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，「范畴与态射」，def:U-cat 后「有些文献将 U-范畴称为局部 U-小范畴」；con:U-small · Checked 2026-10-14
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