terminal object

终对象

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

Translation evidence: Literature usage

Meaning in context

An object T receiving exactly one morphism X→T from every object X of its category.

从范畴任意对象 X 出发，到它的态射恰有一个的对象 T。

Example

Any singleton is terminal in Set\mathbf{Set}.

Usage and distinctions

A one-point space is terminal in Top; the empty set is initial in Set, not terminal.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§3.1, Definition 3.1.11 · 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，「泛性质」，定义 def:universal-objects 中「终对象」 · Checked 2026-10-14
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