Theorems · Definition · category theory
CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex C} →
(h : S.LeftHomologyData) → [inst_2 : S.HasLeftHomology] → S.leftHomology ≅ h.HThe isomorphism S.leftHomology ≅ h.H induced by a left homology data h for a
short complex S.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.ShortComplex.LeftHomologyData.Hstatement · cited by 236
- CategoryTheory.ShortComplex.LeftHomologyDatastatement and proof · cited by 212
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
- CategoryTheory.ShortComplex.leftHomologystatement · cited by 66
- CategoryTheory.ShortComplex.leftHomologyMapIso'proof · cited by 6
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.LeftHomologyData.homologyIsoproof · cited by 34
- CategoryTheory.ShortComplex.mapLeftHomologyIsoproof · cited by 5
- CategoryTheory.ShortComplex.leftHomologyOpIsoproof · cited by 4
- CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_homstatement · cited by 3
- CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_invstatement and proof · cited by 1
- CategoryTheory.ShortComplex.LeftHomologyData.π_comp_leftHomologyIso_inv_assocstatement and proof · cited by 1
- CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_hom_comp_leftHomologyIso_invstatement and proof · cited by 1
- CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_comp_homologyIso_invstatement and proof · cited by 1
- CategoryTheory.ShortComplex.LeftHomologyMapData.leftHomologyMap_eqstatement · cited by 1
- CategoryTheory.ShortComplex.leftRightHomologyComparison_eqstatement · cited by 0
- CategoryTheory.ShortComplex.leftHomologyIsoCokernelLiftproof · cited by 0