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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S₁ S₂ : CategoryTheory.ShortComplex C} [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology] (φ : S₁ ⟶ S₂)
  (h₁ : S₁.RightHomologyData) (h₂ : S₂.RightHomologyData) {Z : C} (h : h₂.H ⟶ Z),
  CategoryTheory.CategoryStruct.comp h₁.homologyIso.hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.rightHomologyMap' φ h₁ h₂) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.homologyMap φ)
      (CategoryTheory.CategoryStruct.comp h₂.homologyIso.hom h)
Defined in
Mathlib.Algebra.Homology.ShortComplex.Homology
Cited by
1 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomologyCategoryTheory.ShortComplex.HasHomology
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CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturality · cited by 1ShortComplex.mapHomologyI…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.HasHomology · cited by 253ShortComplex.HasHomologyCategoryTheory.ShortComplex.homology · cited by 216ShortComplex.homologyCategoryTheory.ShortComplex.RightHomologyData · cited by 211ShortComplex.RightHomolog…CategoryTheory.ShortComplex.RightHomologyData.H · cited by 158RightHomologyData.HCategoryTheory.ShortComplex.homologyMap · cited by 83ShortComplex.homologyMapCategoryTheory.ShortComplex.rightHomologyMap' · cited by 39ShortComplex.rightHomolog…CategoryTheory.ShortComplex.RightHomologyData.homologyIso · cited by 27RightHomologyData.homolog…CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_naturality · cited by 3RightHomologyData.rightHo…RightHomologyData.rightHomolo…CITED BYCITES

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