Theorems · Definition · category theory
CategoryTheory.ShortComplex.leftRightHomologyComparison
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(S : CategoryTheory.ShortComplex C) →
[inst_2 : S.HasLeftHomology] → [inst_3 : S.HasRightHomology] → S.leftHomology ⟶ S.rightHomologyIf a short complex S has both a left and right homology,
this is the canonical morphism S.leftHomology ⟶ S.rightHomology.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 33 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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
- CategoryTheory.ShortComplex.leftHomologystatement · cited by 66
- CategoryTheory.ShortComplex.rightHomologystatement · cited by 66
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
- CategoryTheory.ShortComplex.leftRightHomologyComparison'proof · cited by 20
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.leftRightHomologyComparison_facstatement · cited by 2
- CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ιstatement · cited by 2
- CategoryTheory.ShortComplex.leftRightHomologyComparison_eqstatement · cited by 0
- CategoryTheory.ShortComplex.leftRightHomologyComparison_fac_assocstatement and proof · cited by 0
- CategoryTheory.ShortComplex.π_leftRightHomologyComparison_ι_assocstatement and proof · cited by 0
- CategoryTheory.ShortComplex.hasHomology_of_isIsoLeftRightHomologyComparisonstatement and proof · cited by 0