∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {R : CategoryTheory.Functor Cᵒᵖ RingCat} {J : Type u_6}
  [inst_1 : CategoryTheory.Category.{u_5, u_6} J] (F : CategoryTheory.Functor J (PresheafOfModules R))
  [inst_2 :
    ∀ {X Y : Cᵒᵖ} (f : X ⟶ Y),
      CategoryTheory.Limits.PreservesColimit (F.comp (PresheafOfModules.evaluation R Y))
        (ModuleCat.restrictScalars (RingCat.Hom.hom (R.map f)))]
  [inst_3 : ∀ (X : Cᵒᵖ), CategoryTheory.Limits.HasColimit (F.comp (PresheafOfModules.evaluation R X))] {X Y Z : Cᵒᵖ}
  (f : X ⟶ Y) (g : Y ⟶ Z) (j : J),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι (F.comp (PresheafOfModules.evaluation R X)) j)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.colimMap
          (F.whiskerLeft (PresheafOfModules.restriction R (CategoryTheory.CategoryStruct.comp f g))))
        (CategoryTheory.preservesColimitIso
            (ModuleCat.restrictScalars (RingCat.Hom.hom (R.map (CategoryTheory.CategoryStruct.comp f g))))
            (F.comp (PresheafOfModules.evaluation R Z))).inv) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι (F.comp (PresheafOfModules.evaluation R X)) j)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.Limits.colimMap (F.whiskerLeft (PresheafOfModules.restriction R f)))
          (CategoryTheory.preservesColimitIso (ModuleCat.restrictScalars (RingCat.Hom.hom (R.map f)))
              (F.comp (PresheafOfModules.evaluation R Y))).inv)
        (CategoryTheory.CategoryStruct.comp
          ((ModuleCat.restrictScalars (RingCat.Hom.hom (R.map f))).map
            (CategoryTheory.CategoryStruct.comp
              (CategoryTheory.Limits.colimMap (F.whiskerLeft (PresheafOfModules.restriction R g)))
              (CategoryTheory.preservesColimitIso (ModuleCat.restrictScalars (RingCat.Hom.hom (R.map g)))
                  (F.comp (PresheafOfModules.evaluation R Z))).inv))
          ((ModuleCat.restrictScalarsComp' (RingCat.Hom.hom (R.map f)) (RingCat.Hom.hom (R.map g))
                  (RingCat.Hom.hom (R.map (CategoryTheory.CategoryStruct.comp f g))) ⋯).inv.app
            (CategoryTheory.Limits.colimit (F.comp (PresheafOfModules.evaluation R Z))))))