adjunction

伴随对

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

Other names / variants: adjunction pair

Translation evidence: Literature usage

Meaning in context

Functors F:C→D and G:D→C together with bijections Hom_D(FX,Y)≅Hom_C(X,GY) natural in X and Y.

函子 F:C→D、G:D→C 连同在 X、Y 两变元中自然的双射 Hom_D(FX,Y)≅Hom_C(X,GY)。

Example

The free kk-vector-space functor is left adjoint to the underlying-set functor.

Usage and distinctions

Adjoint functors need not be inverse equivalences; the hom-set correspondence is the requirement.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§4.1, Definition 4.1.1 · 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，「伴随函子」，定义 def:adjunction-pair「伴随对」 · Checked 2026-10-14
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