categorical colimit

余极限

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

Other names / variants: inductive limit · 归纳极限

Translation evidence: Literature usage

Meaning in context

For a small diagram, a cocone from which every compatible cocone factors by a unique map of vertices respecting all legs.

对于小图表，一个余锥使任意其他相容余锥都由它经唯一的顶点态射分解，并保持所有余锥边。

Example

The colimit in sets of {0}⊂{0,1}⊂⋯\{0\}\subset\{0,1\}\subset\cdots is N\mathbb N.

Usage and distinctions

Colimits reverse the universal arrow direction; a categorical colimit is not generally a union.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§3.1, Definition 3.1.23; §3.2 Limits in the Category of Sets · 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，「极限」，def:limit 后术语对照表中的「余极限 (colim)」 · Checked 2026-10-14
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