Theorems · Theorem · category theory
CategoryTheory.Triangulated.TStructure.isGE_iff_orthogonal
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} 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]
(t : CategoryTheory.Triangulated.TStructure C) (n₀ n₁ : ℤ),
n₀ + 1 = n₁ → ∀ (X : C), t.IsGE X n₁ ↔ ∀ (Y : C) (f : Y ⟶ X), t.IsLE Y n₀ → f = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
- CategoryTheory.Pretriangulatedstatement and proof · cited by 669
- CategoryTheory.Limits.zero_compproof · cited by 339
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Triangulated.TStructure.isGE₂proof · cited by 1