universal property

泛性质

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

Translation evidence: Literature usage

Meaning in context

A characterization of specified object-and-map data by a unique factorization for every competing compatible object-and-map datum.

用任意其他相容对象及映射资料的唯一分解，刻画指定对象及映射资料的性质。

Example

Maps X→A×BX\to A\times B correspond uniquely to pairs of maps X→AX\to A and X→BX\to B.

Usage and distinctions

The structure maps belong to the data; uniqueness normally means up to a unique compatible isomorphism.

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Definition sources

  1. Tom Leinster — Basic Category Theory (author arXiv edition)Introduction, Examples 0.6–0.7 and Lemma 0.7 · 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」，开头及始终对象之后的「泛性质」段 · Checked 2026-10-14
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