Theorems · Theorem · category theory
CategoryTheory.ShortComplex.homologyOpIso_hom_naturality
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} (φ : S₁ ⟶ S₂) [inst_2 : S₁.HasHomology] [inst_3 : S₂.HasHomology],
CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.homologyMap (CategoryTheory.ShortComplex.opMap φ))
S₁.homologyOpIso.hom =
CategoryTheory.CategoryStruct.comp S₂.homologyOpIso.hom (CategoryTheory.ShortComplex.homologyMap φ).op- Cited by
- 2 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- Quiver.Hom.opstatement · cited by 1,948
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.homologystatement · cited by 216
- CategoryTheory.Iso.hom_inv_id_assocproof · cited by 187
- CategoryTheory.ShortComplex.opstatement · cited by 88
Cited by2
Results whose statement or proof uses this declaration.
- HomologicalComplex.homologyOp_hom_naturalityproof · cited by 1
- CategoryTheory.ShortComplex.homologyOpIso_hom_naturality_assocproof · cited by 0