small category

小范畴

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

Translation evidence: Literature usage

Meaning in context

A category whose objects and all morphisms form sets in the chosen size convention.

在选定大小约定下，其对象和全部态射均构成集合的范畴。

Example

The category of a finite poset is small.

Usage and distinctions

Smallness is relative to a universe when universes are used; locally small is a weaker condition.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.1, Definition 1.1.6 · 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 的「U-小范畴」；固定宇宙约定 con:U-small · Checked 2026-10-14
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