∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  {F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃)}
  {G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)} (adj₂ : F ⊣₂ G) {X₁ : C₁} {X₂ : C₂} {X₃ Y₃ : C₃}
  (f₃ : X₃ ⟶ Y₃) (g : (F.obj X₁).obj X₂ ⟶ X₃),
  adj₂.homEquiv (CategoryTheory.CategoryStruct.comp g f₃) =
    CategoryTheory.CategoryStruct.comp (adj₂.homEquiv g) ((G.obj (Opposite.op X₁)).map f₃)