Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyData.right_homologyIso_eq_left_homologyIso_trans_iso

∀ {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.right.homologyIso = h.left.homologyIso ≪≫ h.iso

Defined in: Mathlib.Algebra.Homology.ShortComplex.Homology
Cited by: 2 results in Mathlib
Foundations: Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.ShortComplex.HasHomology

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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.Homproof · cited by 32,603
CategoryTheory.Iso.homproof · cited by 7,684
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.symmproof · cited by 993
CategoryTheory.Iso.transstatement and proof · cited by 566
CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
CategoryTheory.ShortComplex.LeftHomologyData.Hstatement and proof · cited by 236
CategoryTheory.ShortComplex.homologystatement and proof · cited by 216
CategoryTheory.Iso.extproof · cited by 166

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.HomologyData.left_homologyIso_eq_right_homologyIso_trans_iso_symmproof · cited by 1
CategoryTheory.Abelian.SpectralObject.spectralSequenceHomologyData_right_homologyIso_eq_left_homologyIsoproof · cited by 0