isomorphism in a category

同构

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

Translation evidence: Literature usage

Meaning in context

A morphism $f:X\to Y$ admitting $g:Y\to X$ with $gf=1_X$ and $fg=1_Y$.

存在态射 g:Y→X 满足 gf=1_X、fg=1_Y 的态射 f:X→Y。

Example

$v\mapsto3v$ is an isomorphism in real vector spaces, with inverse $v\mapsto v/3$.

Usage and distinctions

A bijective continuous map need not be an isomorphism in Top; its inverse must be continuous.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Emily Riehl — Category Theory in Context (current second-edition draft)§1.1, Definition 1.1.10 · 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，「范畴与态射」，def:category 后的「同构（可逆）」段 · Checked 2026-10-14

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