∀ {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} {f₁ : X₁ ⟶ Y₁}
  {X₂ Y₂ : C₂} {f₂ : X₂ ⟶ Y₂} {X₃ Y₃ : C₃} {f₃ : X₃ ⟶ Y₃} (sq₁₂ : F.PushoutObjObj f₁ f₂) (sq₁₃ : G.PullbackObjObj f₁ f₃)
  (α : CategoryTheory.Arrow.mk sq₁₂.ι ⟶ CategoryTheory.Arrow.mk f₃),
  CategoryTheory.CategoryStruct.comp ((adj₂.arrowHomEquiv sq₁₂ sq₁₃) α).right sq₁₃.snd = adj₂.homEquiv α.right