Theorems · Definition · category theory
CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex C} →
(h : S.RightHomologyData) → [inst_2 : S.HasRightHomology] → S.rightHomology ≅ h.HThe isomorphism S.rightHomology ≅ h.H induced by a right homology data h for a
short complex S.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 39 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.RightHomologyDatastatement and proof · cited by 211
- CategoryTheory.ShortComplex.RightHomologyData.Hstatement · cited by 158
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
- CategoryTheory.ShortComplex.rightHomologystatement · cited by 66
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
- CategoryTheory.ShortComplex.rightHomologyMapIso'proof · cited by 2
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.RightHomologyData.homologyIsoproof · cited by 27
- CategoryTheory.ShortComplex.mapRightHomologyIsoproof · cited by 5
- CategoryTheory.ShortComplex.rightHomologyOpIsoproof · cited by 3
- CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyιstatement · cited by 3
- CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_ιproof · cited by 2
- CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_ιstatement and proof · cited by 2
- CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_eqstatement · cited by 1
- CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_hom_comp_homologyIso_invstatement and proof · cited by 1
- CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_invstatement and proof · cited by 1
- CategoryTheory.ShortComplex.RightHomologyData.homologyIso_hom_comp_rightHomologyIso_inv_assocstatement and proof · cited by 0
- CategoryTheory.ShortComplex.leftRightHomologyComparison_eqstatement · cited by 0