Theorems · Theorem · category theory

CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality

∀ {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),
  CategoryTheory.CategoryStruct.comp h₁.homologyIso.inv (CategoryTheory.ShortComplex.homologyMap φ) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.rightHomologyMap' φ h₁ h₂) h₂.homologyIso.inv

Defined in: Mathlib.Algebra.Homology.ShortComplex.Homology
Cited by: 3 results in Mathlib
Foundations: Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.ShortComplex.HasHomology CategoryTheory.ShortComplex.HasHomology

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Cites20

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 and proof · cited by 17,999
CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Category.comp_idproof · cited by 2,119
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.cancel_monoproof · cited by 435
CategoryTheory.Iso.inv_hom_idproof · cited by 308
CategoryTheory.Iso.inv_hom_id_assocproof · cited by 275

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.rightHomologyIso_hom_naturalityproof · cited by 1
CategoryTheory.ShortComplex.mapHomologyIso'_hom_naturalityproof · cited by 1
CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_naturality_assocproof · cited by 0