categorical coproduct

余积

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

Translation evidence: Literature usage

Meaning in context

An object with maps from a specified family such that each family of maps into any Y extends uniquely to a map from that object to Y.

配有从指定对象族进入的态射的对象，使到任意 Y 的对应态射族都唯一延拓为从该对象到 Y 的态射。

Example

{2}⊔{2}\{2\}\sqcup\{2\} is a two-element coproduct in sets.

Usage and distinctions

Ordinary union of overlapping sets fails to retain independent maps out of each component.

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，「极限」，有限极限讨论，积与余积的第一项「余积」 · Checked 2026-10-14
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