Theorems · Definition · category theory
CategoryTheory.ShortComplex.rightHomology
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → (S : CategoryTheory.ShortComplex C) → [S.HasRightHomology] → CThe right homology of a short complex,
given by the H field of a chosen right 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.RightHomologyData.Hproof · cited by 158
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
Cited by80
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.rightHomologyιstatement · cited by 30
- CategoryTheory.ShortComplex.rightHomologyMapstatement · cited by 27
- CategoryTheory.ShortComplex.rightHomologyIsostatement · cited by 20
- CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIsostatement · cited by 14
- CategoryTheory.ShortComplex.rightHomologyFunctorproof · cited by 7
- CategoryTheory.ShortComplex.opcyclesIsoRightHomologystatement · cited by 6
- CategoryTheory.ShortComplex.leftRightHomologyComparisonstatement · cited by 6
- CategoryTheory.ShortComplex.mapRightHomologyIsostatement · cited by 5
- CategoryTheory.ShortComplex.leftHomologyOpIsostatement · cited by 4
- CategoryTheory.ShortComplex.RightHomologyData.rightHomologyIso_inv_comp_rightHomologyιstatement · cited by 3
- CategoryTheory.ShortComplex.rightHomologyOpIsostatement · cited by 3
- CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundarystatement · cited by 3