categorical pullback

拉回

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

Other names / variants: fiber product · 纤维积

Translation evidence: Literature usage

Meaning in context

For A→C←B, an object P with maps to A and B making the square commute and universal among such commuting pairs.

对于 A→C←B，带有到 A、B 的态射、使相应方块交换，且对所有这种交换态射对具有唯一分解性质的对象。

Example

For inclusions A,B⊆CA,B\subseteq C, their pullback in sets is A∩BA\cap B.

Usage and distinctions

A commuting square need not be a pullback; the universal property is additional.

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Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§3.1, Definition 3.1.15 · 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，「完备性」，def:completeness 后「纤维积及其对偶版本」定义第一项；非 Hom 函子的同名拉回 · Checked 2026-10-14
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