Theorems · Definition · category theory
CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso
{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.cycles ≅ h.KThe isomorphism S.cycles ≅ h.K induced by a left homology data h for a
short complex S.
- Cited by
- 28 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.Kstatement · cited by 233
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.LeftHomologyDatastatement and proof · cited by 212
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
- CategoryTheory.ShortComplex.cyclesMapIso'proof · cited by 3
Cited by35
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.moduleCatCyclesIsoproof · cited by 20
- CategoryTheory.Abelian.SpectralObject.cyclesIsoproof · cited by 15
- HomologicalComplex.extendCyclesIsoproof · cited by 13
- CategoryTheory.Abelian.SpectralObject.cyclesIsoHproof · cited by 11
- CategoryTheory.ShortComplex.mapCyclesIsoproof · cited by 8
- CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_istatement · cited by 8
- CategoryTheory.ShortComplex.cyclesOpIsoproof · cited by 8
- CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_inv_comp_iCyclesstatement and proof · cited by 7
- CategoryTheory.ShortComplex.LeftHomologyData.homologyπ_comp_homologyIso_homstatement and proof · cited by 5
- CategoryTheory.ShortComplex.LeftHomologyData.π_comp_homologyIso_invstatement and proof · cited by 3
- HomologicalComplex.homologyπ_extendHomologyIso_homproof · cited by 3
- CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyπ_comp_leftHomologyIso_homstatement · cited by 3