∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {A : Type u₃}
  [inst_1 : CategoryTheory.Category.{v₃, u₃} A] [inst_2 : CategoryTheory.Preregular C]
  [inst_3 : CategoryTheory.FinitaryExtensive C] [inst_4 : ∀ (X : C), CategoryTheory.Projective X]
  (X : CategoryTheory.Sheaf (CategoryTheory.coherentTopology C) A),
  (CategoryTheory.Presheaf.coherentExtensiveEquivalence.functor.obj X).obj = X.obj