categorical equalizer

等化子

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

Other names / variants: 差核

Translation evidence: Literature usage

Meaning in context

For parallel f,g:A→B, a map e:E→A with fe=ge universal among maps with that equality.

对于平行态射 f、g:A→B，满足 fe=ge 且对所有满足同样等式的映射具有唯一分解性质的态射 e:E→A。

Example

The equalizer of n↦n2n\mapsto n^2 and n↦nn\mapsto n on Z\mathbb Z is {0,1}↪Z\{0,1\}\hookrightarrow\mathbb Z.

Usage and distinctions

A kernel is a special equalizer in a pointed setting; arbitrary equalizers need not involve zero maps.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§3.1, Definition 3.1.13 · 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」，平行箭头的极限项：「等化子 或差核」 · Checked 2026-10-14
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