∀ {V : Type u_5} [inst : CategoryTheory.Category.{u_4, u_5} V] {W : Type u_2}
  [inst_1 : CategoryTheory.Category.{u_1, u_2} W] (F : CategoryTheory.Functor V W) (G : Type u_3) [inst_2 : Monoid G]
  (M : Action V G),
  { hom := F.map (CategoryTheory.CategoryStruct.id M).hom, comm := ⋯ } =
    CategoryTheory.CategoryStruct.id
      { V := F.obj M.V, ρ := { toFun := fun g => F.map (M.ρ g), map_one' := ⋯, map_mul' := ⋯ } }