Theorems · Theorem · category theory
CategoryTheory.ShortComplex.HomologyData.left_homologyIso_eq_right_homologyIso_trans_iso_symm
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex C} (h : S.HomologyData) [inst_2 : S.HasHomology],
h.left.homologyIso = h.right.homologyIso ≪≫ h.iso.symm- Cited by
- 1 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.
Cites20
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
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Iso.symmstatement and proof · cited by 993
- CategoryTheory.Iso.transstatement and proof · cited by 566
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.LeftHomologyData.Hstatement · cited by 236
- CategoryTheory.ShortComplex.homologystatement and proof · cited by 216
- CategoryTheory.ShortComplex.RightHomologyData.Hstatement and proof · cited by 158
- CategoryTheory.ShortComplex.HomologyData.leftstatement and proof · cited by 130
- CategoryTheory.ShortComplex.HomologyDatastatement and proof · cited by 102
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.SpectralObject.EIsoH_hom_opcyclesIsoH_invproof · cited by 1