Theorems · Theorem · category theory
CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id_assoc
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] {X₁ X₂ X₃ : CochainComplex C ℤ} (f : X₁ ⟶ X₂) (g : X₂ ⟶ X₃)
{Z : CochainComplex C ℤ} (h : CochainComplex.mappingCone g ⟶ Z),
CategoryTheory.CategoryStruct.comp (CochainComplex.MappingConeCompHomotopyEquiv.hom f g)
(CategoryTheory.CategoryStruct.comp (CochainComplex.MappingConeCompHomotopyEquiv.inv f g) h) =
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- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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.Category.assocproof · cited by 6,433
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Category.id_compproof · cited by 1,998
- HomologicalComplex.Xstatement · cited by 1,839
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- CategoryTheory.Pretriangulated.Triangle.obj₁statement · cited by 360
- CategoryTheory.Pretriangulated.Triangle.obj₂statement · cited by 316
- CategoryTheory.Pretriangulated.Triangle.mor₁statement · cited by 190
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