∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) (obj : C → D) (e : (X : C) → F.obj X ≅ obj X),
  F.copyObj obj e =
    { obj := obj,
      map := fun {X Y} f =>
        CategoryTheory.CategoryStruct.comp (e X).inv (CategoryTheory.CategoryStruct.comp (F.map f) (e Y).hom),
      map_id := ⋯, map_comp := ⋯ }