Theorems · Definition · category theory
CategoryTheory.ShortComplex.HomologyData.left
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex C} → S.HomologyData → S.LeftHomologyDataa left homology data
- Cited by
- 130 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 6 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.LeftHomologyDatastatement · cited by 212
- CategoryTheory.ShortComplex.HomologyDatastatement and proof · cited by 102
Cited by165
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.homologyproof · cited by 216
- CategoryTheory.ShortComplex.HomologyData.isostatement · cited by 45
- CategoryTheory.ShortComplex.leftHomologyIsoproof · cited by 27
- CategoryTheory.ShortComplex.HomologyMapData.leftstatement · cited by 25
- CategoryTheory.ShortComplex.exact_of_isoproof · cited by 18
- CategoryTheory.ShortComplex.homologyMap'statement and proof · cited by 16
- CategoryTheory.Abelian.SpectralObject.EIsoHproof · cited by 14
- HomologicalComplex.extendCyclesIsoproof · cited by 13
- HomologicalComplex.extendHomologyIsoproof · cited by 13
- CategoryTheory.ShortComplex.mapHomologyIsoproof · cited by 12
- CategoryTheory.ShortComplex.exact_iff_of_epi_of_isIso_of_monoproof · cited by 11
- CategoryTheory.Abelian.SpectralObject.cyclesIsoHproof · cited by 11