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Source labels openChecked July 26, 2026

MathOverflowCategory theory

Mathoverflow 31809

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

Mathematical statement

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

Statement source: MathOverflow statement material

Statement terms: CC-BY-SA-4.0

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Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

mathoverflow_31809

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem mathoverflow_31809 : answer(sorry)  ( (C : Type*) [Category C] [Preadditive C]    [HasZeroObject C] [HasShift C ] [ (n : ), (shiftFunctor C n).Additive]    [Pretriangulated C], IsTriangulated C) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References