∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u} [inst_1 : CategoryTheory.Category.{v, u} D]
  {x y : C} (f : x ⟶ y) (F : CategoryTheory.Functor C D),
  CategoryTheory.nerve.homEquiv ((CategoryTheory.nerve.edgeMk f).map (CategoryTheory.nerveMap F)) = F.map f