-- Module: Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
R : CategoryTheory.Functor.{v_1, u, u_1, u + 1} Cᵒᵖ CommRingCat
M :
  PresheafOfModules
    (R ⋙
      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
        RingCat.carrier))
X Y : Cᵒᵖ
f : X ⟶ Y
m : (↑(M.obj X) : Type u)
hf :
  Eq (α :=
    (↑((ModuleCat.restrictScalars (CommRingCat.Hom.hom (R.map f))).obj
          (MonoidalCategoryStruct.tensorObj (𝒞 :=
            ModuleCat.moduleCategory
              (↑(Functor.obj
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier))
                    Y) :
                Type u))
            ((unit
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))).obj
              Y)
            (M.obj Y))) :
      Type u))
    ((ConcreteCategory.hom (FC := fun (x1 x2 : ModuleCat (↑(R.obj Y) : Type u)) ↦
            LinearMap (R := (↑(R.obj Y) : Type u)) (RingHom.id (↑(R.obj Y) : Type u)) (↑x1 : Type u) (↑x2 : Type u))
            (CC := ModuleCat.carrier) (Y :=
            MonoidalCategoryStruct.tensorObj (𝒞 :=
              ModuleCat.moduleCategory
                (↑(Functor.obj
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier))
                      Y) :
                  Type u))
              ((unit
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier))).obj
                Y)
              (M.obj Y))
            (Iso.inv (λ_ (M.obj Y))) :
          (a : (↑(M.obj Y) : Type u)) → (↑((unit (R ⋙ forget₂ CommRingCat RingCat)).obj Y ⊗ M.obj Y) : Type u))
        ((ModuleCat.Hom.hom (M.map f) :
            (a : (↑(M.obj X) : Type u)) →
              (↑((ModuleCat.restrictScalars (CommRingCat.Hom.hom (R.map f))).obj (M.obj Y)) : Type u))
          m) :
      (↑(MonoidalCategoryStruct.tensorObj (𝒞 :=
            ModuleCat.moduleCategory
              (↑(Functor.obj
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier))
                    Y) :
                Type u))
            ((unit
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))).obj
              Y)
            (M.obj Y)) :
        Type u))
    ((ModuleCat.Hom.hom
            ((Monoidal.tensorObj
                  (unit
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier)))
                  M).map
              f) :
          (a : (↑((unit (R ⋙ forget₂ CommRingCat RingCat)).obj X ⊗ M.obj X) : Type u)) →
            (↑((ModuleCat.restrictScalars (CommRingCat.Hom.hom (R.map f))).obj
                  ((unit (R ⋙ forget₂ CommRingCat RingCat)).obj Y ⊗ M.obj Y)) :
              Type u))
        ((ModuleCat.Hom.hom (Iso.inv (λ_ (M.obj X))) :
            (a : (↑(M.obj X) : Type u)) → (↑((unit (R ⋙ forget₂ CommRingCat RingCat)).obj X ⊗ M.obj X) : Type u))
          m) :
      (↑((ModuleCat.restrictScalars (CommRingCat.Hom.hom (R.map f))).obj
            (MonoidalCategoryStruct.tensorObj (𝒞 :=
              ModuleCat.moduleCategory
                (↑(Functor.obj
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier))
                      Y) :
                  Type u))
              ((unit
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier))).obj
                Y)
              (M.obj Y))) :
        Type u))
⊢ Eq (α :=
    (↑(Functor.obj
          (ModuleCat.restrictScalars
            (RingCat.Hom.hom
              (CategoryTheory.Functor.map
                (R ⋙
                  forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                    CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                    (CD := RingCat.carrier))
                f)))
          ((Monoidal.tensorObj
                (unit
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier)))
                M).obj
            Y)) :
      Type u))
    ((ModuleCat.Hom.hom
            (M.map f ≫
              CategoryTheory.Functor.map
                (ModuleCat.restrictScalars
                  (RingCat.Hom.hom
                    (CategoryTheory.Functor.map
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier))
                      f)))
                (Iso.hom
                  ((fun (x : Cᵒᵖ) ↦
                      (Iso.symm (λ_ (M.obj x)) :
                        M.obj x ≅
                          MonoidalCategoryStruct.tensorObj (𝒞 :=
                            ModuleCat.moduleCategory
                              (↑(Functor.obj
                                    (R ⋙
                                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                        (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                        fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                        RingCat.carrier))
                                    x) :
                                Type u))
                            ((𝟙_
                                (ModuleCat
                                  (↑(Functor.obj
                                        (R ⋙
                                          forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                            (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                            fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                            RingCat.carrier))
                                        x) :
                                    Type u)))
                              (𝒞 :=
                              ModuleCat.moduleCategory
                                (↑(Functor.obj
                                      (R ⋙
                                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                          (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                          fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                          RingCat.carrier))
                                      x) :
                                  Type u)))
                            (M.obj x)))
                    Y))) :
          (a : (↑(M.obj X) : Type u)) →
            (↑((ModuleCat.restrictScalars (RingCat.Hom.hom ((R ⋙ forget₂ CommRingCat RingCat).map f))).obj
                  ((Monoidal.tensorObj (unit (R ⋙ forget₂ CommRingCat RingCat)) M).obj Y)) :
              Type u))
        m :
      (↑(Functor.obj
            (ModuleCat.restrictScalars
              (RingCat.Hom.hom
                (CategoryTheory.Functor.map
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))
                  f)))
            ((Monoidal.tensorObj
                  (unit
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier)))
                  M).obj
              Y)) :
        Type u))
    ((ModuleCat.Hom.hom
            (Iso.hom
                ((fun (x : Cᵒᵖ) ↦
                    (Iso.symm (λ_ (M.obj x)) :
                      M.obj x ≅
                        MonoidalCategoryStruct.tensorObj (𝒞 :=
                          ModuleCat.moduleCategory
                            (↑(Functor.obj
                                  (R ⋙
                                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                      (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                      fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                      RingCat.carrier))
                                  x) :
                              Type u))
                          ((𝟙_
                              (ModuleCat
                                (↑(Functor.obj
                                      (R ⋙
                                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                          (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                          fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                          RingCat.carrier))
                                      x) :
                                  Type u)))
                            (𝒞 :=
                            ModuleCat.moduleCategory
                              (↑(Functor.obj
                                    (R ⋙
                                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                        (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                        fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                        RingCat.carrier))
                                    x) :
                                Type u)))
                          (M.obj x)))
                  X) ≫
              (Monoidal.tensorObj
                    (unit
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier)))
                    M).map
                f) :
          (a : (↑(M.obj X) : Type u)) →
            (↑((ModuleCat.restrictScalars (RingCat.Hom.hom ((R ⋙ forget₂ CommRingCat RingCat).map f))).obj
                  ((Monoidal.tensorObj (unit (R ⋙ forget₂ CommRingCat RingCat)) M).obj Y)) :
              Type u))
        m :
      (↑(Functor.obj
            (ModuleCat.restrictScalars
              (RingCat.Hom.hom
                (CategoryTheory.Functor.map
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))
                  f)))
            ((Monoidal.tensorObj
                  (unit
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier)))
                  M).obj
              Y)) :
        Type u))

Tactic:
dsimp [CommRingCat.forgetToRingCat_obj]

Premises used: CommRingCat.forgetToRingCat_obj