stylistic:tone, quality:correction
counit–unit adjunction induces hom-set adjunction

Given functors F : D → C, G : C → D, and a counit–unit adjunction (ε, η) : F ⊣ {\displaystyle \dashv } G, we can construct a hom-set adjunction by finding the natural transformation Φ : hom (F -,-) → hom (-, G -) in the following steps: