31809.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Mathoverflow 31809

Source: Mathoverflow/31809

References:

[CLLZ26] X.-W. Chen, J. Liu, X.-S. Lu and C. Zhang, "A pre-triangulated category which is not triangulated", arXiv:2608.09777

Imports (1)

FormalConjecturesUtil

theorem Mathoverflow31809.mathoverflow_31809 Does there exist a category that is pretriangulated but not triangulated? sorry line 44 source
Source documentation
Does there exist a category that is pretriangulated but not triangulated?
Yes. Theorem 1.2 of [CLLZ26] twists the triangulated structure on the category of finitely generated projective modules over the preprojective algebra of type $A_5$ over $\mathbb{F}_2$. The result is pretriangulated but does not satisfy the octahedral axiom.

depends on sorry what this means
Statement uses: Iff, True, Not, CategoryTheory.Category, CategoryTheory.Preadditive, CategoryTheory.Limits.HasZeroObject, CategoryTheory.HasShift, Int, CategoryTheory.Functor.Additive, CategoryTheory.shiftFunctor, CategoryTheory.Pretriangulated, CategoryTheory.IsTriangulated
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem mathoverflow_31809 : answer(True) ↔ ¬ (∀ (C : Type*) [Category C] [Preadditive C]
    [HasZeroObject C] [HasShift C ℤ] [∀ (n : ℤ), (shiftFunctor C n).Additive]
    [Pretriangulated C], IsTriangulated C) := by
…
```