unit of an adjunction

单位

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

Translation evidence: Literature usage

Meaning in context

For F⊣GF\dashv G, the natural transformation η:1C⇒GF\eta:1_C\Rightarrow GF whose component corresponds to 1FX1_{FX} under the adjunction bijection.

对于 F⊣G，由伴随双射把 1_FX 对应到 η_X:X→GFX 而组成的自然变换 η:1_C⇒GF。

Example

For free vector spaces, ηS(s)=es\eta_S(s)=e_s.

Usage and distinctions

Unit here belongs to an adjunction; it is not the multiplicative identity of a ring.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Emily Riehl — Category Theory in Context (current second-edition draft)§4.2, Lemma 4.2.2 · 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-unit-counit「单位」 · Checked 2026-10-14
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