Theorems · Definition · category theory
CategoryTheory.ShortComplex.leftHomology
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → (S : CategoryTheory.ShortComplex C) → [S.HasLeftHomology] → CThe left homology of a short complex, given by the H field of a chosen left homology data.
- Cited by
- 66 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.LeftHomologyData.Hproof · cited by 236
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.leftHomologyDataproof · cited by 83
Cited by80
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.leftHomologyπstatement · cited by 29
- CategoryTheory.ShortComplex.leftHomologyMapstatement · cited by 28
- CategoryTheory.ShortComplex.leftHomologyIsostatement · cited by 27
- CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIsostatement · cited by 13
- CategoryTheory.ShortComplex.leftHomologyFunctorproof · cited by 7
- CategoryTheory.ShortComplex.leftRightHomologyComparisonstatement · cited by 6
- CategoryTheory.ShortComplex.cyclesIsoLeftHomologystatement · cited by 6
- CategoryTheory.ShortComplex.mapLeftHomologyIsostatement · cited by 5
- CategoryTheory.ShortComplex.leftHomologyOpIsostatement · cited by 4
- CategoryTheory.ShortComplex.homologyπ_comp_leftHomologyIso_inv_assocstatement and proof · cited by 4
- CategoryTheory.ShortComplex.rightHomologyOpIsostatement · cited by 3
- CategoryTheory.ShortComplex.LeftHomologyData.homologyIso_leftHomologyDatastatement · cited by 3