Mathoverflow 31809

Source: Mathoverflow/31809

theorem Mathoverflow31809.mathoverflow_31809 : (∀ (C : Type u_1) [inst : CategoryTheory.Category.{u_2, u_1} C] [inst_1 : CategoryTheory.Preadditive C] [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.HasShift C ℤ] [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C], CategoryTheory.IsTriangulated C) ↔ sorry

Does there exist a category that is pretriangulated but not triangulated?