Theorems · Theorem · category theory

CategoryTheory.ShortComplex.rightHomologyIso_hom_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),
  CategoryTheory.CategoryStruct.comp S₁.rightHomologyIso.hom (CategoryTheory.ShortComplex.homologyMap φ) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.rightHomologyMap φ) S₂.rightHomologyIso.hom

Defined in: Mathlib.Algebra.Homology.ShortComplex.Homology
Cited by: 1 results in Mathlib
Foundations: Depth 45 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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Cites17

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.homstatement · cited by 7,684
CategoryTheory.Iso.invproof · cited by 6,514
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 and proof · cited by 83
CategoryTheory.ShortComplex.rightHomologystatement · cited by 66
CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.rightHomologyIso_hom_naturality_assocproof · cited by 1