Theorems · Theorem · category theory
CategoryTheory.ShortComplex.leftHomologyMap_op
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} (φ : S₁ ⟶ S₂) [inst_2 : S₁.HasLeftHomology] [inst_3 : S₂.HasLeftHomology],
(CategoryTheory.ShortComplex.leftHomologyMap φ).op =
CategoryTheory.CategoryStruct.comp S₂.rightHomologyOpIso.inv
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.ShortComplex.rightHomologyMap (CategoryTheory.ShortComplex.opMap φ)) S₁.rightHomologyOpIso.hom)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.Iso.invstatement · cited by 6,514
- 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 · cited by 1,948
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
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