Theorems · Theorem · category theory
CategoryTheory.ShortComplex.homologyMap_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ S₃ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology]
[inst_4 : S₃.HasHomology] (φ₁ : S₁ ⟶ S₂) (φ₂ : S₂ ⟶ S₃),
CategoryTheory.ShortComplex.homologyMap (CategoryTheory.CategoryStruct.comp φ₁ φ₂) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.homologyMap φ₁)
(CategoryTheory.ShortComplex.homologyMap φ₂)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.homologystatement · cited by 216
- CategoryTheory.ShortComplex.homologyMapstatement · cited by 83
- CategoryTheory.ShortComplex.homologyDataproof · cited by 33
- CategoryTheory.ShortComplex.homologyMap'_compproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- HomologicalComplex.homologyMap_compproof · cited by 7
- CategoryTheory.Abelian.SpectralObject.map_compproof · cited by 4
- HomologicalComplex.homologyπ_restrictionHomologyIso_homproof · cited by 2
- HomologicalComplex.restrictionHomologyIso_inv_homologyιproof · cited by 1