Theorems · Theorem · category theory
CategoryTheory.Triangulated.TStructure.le_of_isLE
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, 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]
(t : CategoryTheory.Triangulated.TStructure C) (X : C) (n : ℤ) [t.IsLE X n], t.le n X- Cited by
- 5 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- 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.Triangulated.TStructurestatement and proof · cited by 318
- CategoryTheory.Triangulated.TStructure.IsLEstatement and proof · cited by 48
- CategoryTheory.Triangulated.TStructure.lestatement · cited by 14
- CategoryTheory.Triangulated.TStructure.IsLE.leproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Triangulated.TStructure.zeroproof · cited by 7
- CategoryTheory.Triangulated.TStructure.isLE_shiftproof · cited by 6
- CategoryTheory.Triangulated.TStructure.isLE_of_isoproof · cited by 4
- CategoryTheory.Triangulated.TStructure.isLE_of_leproof · cited by 4
- CategoryTheory.Triangulated.TStructure.le_iff_isLEproof · cited by 0