Theorems · Theorem · category theory
CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality
∀ {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.CategoryStruct.comp (CategoryTheory.ShortComplex.cyclesMap φ).op S₁.opcyclesOpIso.inv =
CategoryTheory.CategoryStruct.comp S₂.opcyclesOpIso.inv
(CategoryTheory.ShortComplex.opcyclesMap (CategoryTheory.ShortComplex.opMap φ))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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.homproof · cited by 7,684
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Category.comp_idproof · cited by 2,119
- Quiver.Hom.opstatement and proof · cited by 1,948
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.Iso.hom_inv_idproof · cited by 264
Cited by2
Results whose statement or proof uses this declaration.
- HomologicalComplex.opcyclesOpIso_inv_naturalityproof · cited by 1
- CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality_assocproof · cited by 0