Theorems · Definition · category theory
CategoryTheory.ShortComplex.leftHomologyData
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(S : CategoryTheory.ShortComplex C) → [S.HasLeftHomology] → S.LeftHomologyDataA chosen S.LeftHomologyData for a short complex S that has left homology
- Cited by
- 83 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Nonempty.someproof · cited by 340
- CategoryTheory.ShortComplex.LeftHomologyDatastatement · cited by 212
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.HasLeftHomology.conditionproof · cited by 0
Cited by109
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.cyclesproof · cited by 220
- CategoryTheory.ShortComplex.iCyclesproof · cited by 100
- CategoryTheory.ShortComplex.leftHomologyproof · cited by 66
- CategoryTheory.ShortComplex.toCyclesproof · cited by 47
- CategoryTheory.ShortComplex.cyclesMapproof · cited by 42
- CategoryTheory.ShortComplex.liftCyclesproof · cited by 32
- CategoryTheory.ShortComplex.leftHomologyπproof · cited by 29
- CategoryTheory.ShortComplex.leftHomologyMapproof · cited by 28
- CategoryTheory.ShortComplex.LeftHomologyData.cyclesIsoproof · cited by 28
- CategoryTheory.ShortComplex.leftHomologyIsoproof · cited by 27
- groupHomology.isoCycles₁proof · cited by 19
- groupCohomology.isoCocycles₁proof · cited by 19