∀ {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))
  (c : CategoryTheory.Limits.Cocone F)
  (hc : (X : Cᵒᵖ) → CategoryTheory.Limits.IsColimit ((PresheafOfModules.evaluation R X).mapCocone c))
  (s : CategoryTheory.Limits.Cocone F) {X Y : Cᵒᵖ} (f : X ⟶ Y) (j : J),
  CategoryTheory.CategoryStruct.comp (((PresheafOfModules.evaluation R X).mapCocone c).ι.app j)
      (CategoryTheory.CategoryStruct.comp (c.pt.map f)
        ((ModuleCat.restrictScalars (RingCat.Hom.hom (R.map f))).map
          ((hc Y).desc ((PresheafOfModules.evaluation R Y).mapCocone s)))) =
    CategoryTheory.CategoryStruct.comp (((PresheafOfModules.evaluation R X).mapCocone c).ι.app j)
      (CategoryTheory.CategoryStruct.comp ((hc X).desc ((PresheafOfModules.evaluation R X).mapCocone s)) (s.pt.map f))