Theorems · Theorem · category theory
CochainComplex.homologyMap_comp_eq_zero_of_distTriang
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : HasDerivedCategory C] (T : CategoryTheory.Pretriangulated.Triangle (CochainComplex C ℤ)),
DerivedCategory.Q.mapTriangle.obj T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles →
∀ (n : ℤ),
CategoryTheory.CategoryStruct.comp (HomologicalComplex.homologyMap T.mor₁ n)
(HomologicalComplex.homologyMap T.mor₂ n) =
0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upstatement and proof · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
Cited by2
Results whose statement or proof uses this declaration.
- CochainComplex.homologyMap_comp_eq_zero_of_distTriang_assocproof · cited by 0
- CochainComplex.homologyMap_exact₂_of_distTriangstatement · cited by 0