initial object

始对象

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

Translation evidence: Literature usage

Meaning in context

An object I having exactly one morphism I→X to every object X of its category.

到范畴任意对象 X 的态射恰有一个的对象 I。

Example

∅\emptyset is initial in Set\mathbf{Set}.

Usage and distinctions

Initial does not mean a least element unless the category is a poset category.

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 · 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「始对象」 · Checked 2026-10-14
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