Theorems · Definition · category theory
CategoryTheory.ShortComplex.homologyData
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(S : CategoryTheory.ShortComplex C) → [S.HasHomology] → S.HomologyDataA chosen S.HomologyData for a short complex S that has homology
- Cited by
- 33 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.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.HomologyDatastatement · cited by 102
- CategoryTheory.ShortComplex.HasHomology.conditionproof · cited by 0
Cited by42
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.homologyproof · cited by 216
- CategoryTheory.ShortComplex.homologyMapproof · cited by 83
- CategoryTheory.ShortComplex.leftHomologyIsoproof · cited by 27
- CategoryTheory.ShortComplex.rightHomologyIsoproof · cited by 20
- HomologicalComplex.extendCyclesIsoproof · cited by 13
- HomologicalComplex.extendHomologyIsoproof · cited by 13
- CategoryTheory.ShortComplex.mapHomologyIsoproof · cited by 12
- HomologicalComplex.extendOpcyclesIsoproof · cited by 9
- CategoryTheory.ShortComplex.mapHomologyIso'proof · cited by 7
- CategoryTheory.ShortComplex.exact_iff_isZero_homologyproof · cited by 6
- CategoryTheory.ShortComplex.leftRightHomologyComparison'_facproof · cited by 4
- CategoryTheory.ShortComplex.quasiIso_opMap_iffproof · cited by 4