∀ {V : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} V] {G : Type u_2} [inst_1 : Monoid G]
  (F : CategoryTheory.Functor (CategoryTheory.SingleObj G) V) (g : G),
  (Action.FunctorCategoryEquivalence.inverse.obj F).ρ g = F.map g