∀ {k G : Type u_1} [inst : CommRing k] [inst_1 : Group G] {X Y : Action (FGModuleCat k) G}
  (X' : Action (FGModuleCat k) G) (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft ((Action.forget (FGModuleCat k) G).obj X')
        ((Action.forget (FGModuleCat k) G).map f))
      ({ εIso := CategoryTheory.Iso.refl (CategoryTheory.MonoidalCategoryStruct.tensorUnit (FGModuleCat k)),
              μIso := fun x x_1 =>
                CategoryTheory.Iso.refl
                  (CategoryTheory.MonoidalCategoryStruct.tensorObj ((Action.forget (FGModuleCat k) G).obj x)
                    ((Action.forget (FGModuleCat k) G).obj x_1)),
              μIso_hom_natural_left := ⋯, μIso_hom_natural_right := ⋯, associativity := ⋯, left_unitality := ⋯,
              right_unitality := ⋯ }.μIso
          X' Y).hom =
    CategoryTheory.CategoryStruct.comp
      ({ εIso := CategoryTheory.Iso.refl (CategoryTheory.MonoidalCategoryStruct.tensorUnit (FGModuleCat k)),
              μIso := fun x x_1 =>
                CategoryTheory.Iso.refl
                  (CategoryTheory.MonoidalCategoryStruct.tensorObj ((Action.forget (FGModuleCat k) G).obj x)
                    ((Action.forget (FGModuleCat k) G).obj x_1)),
              μIso_hom_natural_left := ⋯, μIso_hom_natural_right := ⋯, associativity := ⋯, left_unitality := ⋯,
              right_unitality := ⋯ }.μIso
          X' X).hom
      ((Action.forget (FGModuleCat k) G).map (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X' f))