∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {G : Type u₂} [inst_1 : CategoryTheory.Groupoid G]
  (F : CategoryTheory.Functor G (CategoryTheory.Core C)) {X Y : G} (f : X ⟶ Y),
  (CategoryTheory.Core.forgetFunctorToCore.obj F).map f = (F.map f).iso.hom