categorical limit

极限

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

Other names / variants: projective limit · 投射极限 · inverse limit · 逆向极限

Translation evidence: Literature usage

Meaning in context

For a small diagram D:J→C, a cone through which every other cone factors by a unique vertex map respecting all legs.

对于小图表 D:J→C，一个锥使任意其他锥都通过唯一的顶点态射分解，并保持所有锥边。

Example

A pullback of 2a2a and 3b3b on integers is {(3k,2k):k∈Z}\{(3k,2k):k\in\mathbb Z\}.

Usage and distinctions

Li’s table uses 极限 for lim and 余极限 for colim; inverse limit may also denote a particular inverse-system shape.

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Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§3.1, cone and limit definitions; §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「极限 (lim)」 · Checked 2026-10-14
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