equivalence of categories
范畴等价
Meaning in context
A functor F:C→D with a functor G:D→C and natural isomorphisms GF≅1_C and FG≅1_D.
具有拟逆函子 G 且 GF 与恒等函子、FG 与恒等函子分别自然同构的函子 F:C→D。
Example
Finite-dimensional -vector spaces are equivalent to the category of natural-number dimensions and matrices.
Usage and distinctions
Equivalence allows composites naturally isomorphic to identities; isomorphism of categories requires actual inverse functors.
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Recommended reading in this subject · Preparation & skip guidance
Definition sources
- Emily Riehl — Category Theory in Context (current second-edition draft)§1.5, Definition 1.5.4 · Checked 2026-10-14
Translation sources
- 李文威 — 代数学方法，第一卷（作者源码）第2章，「函子与自然变换」，def:equivalence 与范畴等价判别；源码中的「范畴等价」 · Checked 2026-10-14