categorical product

积

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

Translation evidence: Literature usage

Meaning in context

Objects P with projections to a specified family such that every matching family of maps from any X arises uniquely from a map X→P.

配有到指定对象族的投影的对象 P，使从任意 X 出发的相应映射族都唯一来自 X→P 的态射。

Example

The product of sets {2}\{2\} and {5,7}\{5,7\} has two ordered pairs.

Usage and distinctions

The product includes its projections; in a poset it is a greatest lower bound.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§3.1, Definition 3.1.9 · 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 · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.