Theorems · Definition · category theory
CategoryTheory.ShortComplex.rightHomologyIso
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(S : CategoryTheory.ShortComplex C) → [inst_2 : S.HasHomology] → S.rightHomology ≅ S.homologyWhen a short complex has homology, this is the canonical isomorphism
S.rightHomology ≅ S.homology.
- Cited by
- 20 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.
Cites15
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.symmproof · cited by 993
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.ShortComplex.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.homologystatement · cited by 216
- CategoryTheory.ShortComplex.HomologyData.rightproof · cited by 99
- CategoryTheory.ShortComplex.rightHomologystatement · cited by 66
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
Cited by25
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.homologyιproof · cited by 51
- CategoryTheory.ShortComplex.RightHomologyData.homologyIsoproof · cited by 27
- CategoryTheory.ShortComplex.homologyι_comp_fromOpcyclesproof · cited by 11
- CategoryTheory.ShortComplex.homologyι_naturalityproof · cited by 7
- CategoryTheory.ShortComplex.homologyOpIsoproof · cited by 5
- CategoryTheory.ShortComplex.homologyIsKernelproof · cited by 4
- CategoryTheory.ShortComplex.homology_π_ιproof · cited by 4
- CategoryTheory.ShortComplex.RightHomologyData.homologyIso_rightHomologyDatastatement and proof · cited by 3
- CategoryTheory.ShortComplex.leftRightHomologyComparison_facstatement · cited by 2
- CategoryTheory.ShortComplex.rightHomologyIso_hom_comp_homologyιstatement and proof · cited by 2
- CategoryTheory.ShortComplex.homologyMap_opproof · cited by 2
- CategoryTheory.ShortComplex.homologyι_descOpcycles_eq_zero_of_boundaryproof · cited by 2