Theorems · Theorem · category theory
HomotopyCategory.mappingCone_triangleh_distinguished
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] [inst_3 : CategoryTheory.Limits.HasZeroObject C]
{X Y : CochainComplex C ℤ} (f : X ⟶ Y),
CochainComplex.mappingCone.triangleh f ∈ CategoryTheory.Pretriangulated.distinguishedTriangles- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
- CategoryTheory.Pretriangulated.distinguishedTrianglesstatement · cited by 316
- CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
- HomotopyCategorystatement · cited by 132
Cited by1
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.quasiIso_descShortComplexproof · cited by 1