∀ (R : Type u_1) [inst : CommRing R] {X₁ Y₁ X₂ Y₂ : CoalgCat R} (f : X₁ ⟶ Y₁) (g : X₂ ⟶ Y₂),
  (CategoryTheory.forget₂ (CoalgCat R) (ModuleCat R)).map (CategoryTheory.MonoidalCategoryStruct.tensorHom f g) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Iso.refl
          (CategoryTheory.MonoidalCategoryStruct.tensorObj ((CategoryTheory.forget₂ (CoalgCat R) (ModuleCat R)).obj X₁)
            ((CategoryTheory.forget₂ (CoalgCat R) (ModuleCat R)).obj X₂))).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.tensorHom ((CategoryTheory.forget₂ (CoalgCat R) (ModuleCat R)).map f)
          ((CategoryTheory.forget₂ (CoalgCat R) (ModuleCat R)).map g))
        (CategoryTheory.Iso.refl
            (CategoryTheory.MonoidalCategoryStruct.tensorObj
              ((CategoryTheory.forget₂ (CoalgCat R) (ModuleCat R)).obj Y₁)
              ((CategoryTheory.forget₂ (CoalgCat R) (ModuleCat R)).obj Y₂))).hom)