∀ {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 Y₁ : C₁} {X₂ : C₂} {X₃ : C₃}
  (f₁ : X₁ ⟶ Y₁) (g : (F.obj Y₁).obj X₂ ⟶ X₃) {Z : C₂} (h : (G.obj (Opposite.op X₁)).obj X₃ ⟶ Z),
  CategoryTheory.CategoryStruct.comp (adj₂.homEquiv (CategoryTheory.CategoryStruct.comp ((F.map f₁).app X₂) g)) h =
    CategoryTheory.CategoryStruct.comp (adj₂.homEquiv g) (CategoryTheory.CategoryStruct.comp ((G.map f₁.op).app X₃) h)