Theorems · Inductive type · category theory
CategoryTheory.ShortComplex.HasLeftHomology
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → CategoryTheory.ShortComplex C → PropA short complex S has left homology when there exists a S.LeftHomologyData
- Cited by
- 132 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
- CategoryTheory.ShortComplexstatement · cited by 1,850
Cited by162
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.cyclesstatement and proof · cited by 220
- CategoryTheory.ShortComplex.iCyclesstatement and proof · cited by 100
- CategoryTheory.ShortComplex.leftHomologyDatastatement and proof · cited by 83
- CategoryTheory.ShortComplex.leftHomologystatement and proof · cited by 66
- CategoryTheory.ShortComplex.toCyclesstatement and proof · cited by 47
- CategoryTheory.ShortComplex.cyclesMapstatement and proof · cited by 42
- CategoryTheory.ShortComplex.liftCyclesstatement and proof · cited by 32
- CategoryTheory.ShortComplex.leftHomologyπstatement and proof · cited by 29
- CategoryTheory.ShortComplex.leftHomologyMapstatement and proof · cited by 28
- CategoryTheory.ShortComplex.LeftHomologyData.cyclesIsostatement and proof · cited by 28
- CategoryTheory.ShortComplex.liftCycles_istatement and proof · cited by 18
- CategoryTheory.ShortComplex.toCycles_istatement and proof · cited by 16