Theorems · Theorem · category theory
CategoryTheory.ShortComplex.homologyMap_op
∀ {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.ShortComplex.homologyMap φ).op =
CategoryTheory.CategoryStruct.comp S₂.homologyOpIso.inv
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.ShortComplex.homologyMap (CategoryTheory.ShortComplex.opMap φ)) S₁.homologyOpIso.hom)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- Quiver.Hom.opstatement and proof · cited by 1,948
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.homologyOpIso_hom_naturalityproof · cited by 2
- CategoryTheory.ShortComplex.homologyOpIso_inv_naturalityproof · cited by 1