Theorems · Theorem · category theory
CategoryTheory.ShortComplex.RightHomologyData.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)
(h₁ : S₁.RightHomologyData) (h₂ : S₂.RightHomologyData),
CategoryTheory.CategoryStruct.comp h₁.homologyIso.hom (CategoryTheory.ShortComplex.rightHomologyMap' φ h₁ h₂) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.homologyMap φ) h₂.homologyIso.hom- Cited by
- 3 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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 and proof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.Iso.inv_hom_id_assocproof · cited by 275
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.LeftHomologyData.Hproof · cited by 236
Cited by3
Results whose statement or proof uses this declaration.