Theorems · Definition · category theory
CategoryTheory.ShortComplex.LeftHomologyData.i
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex C} → (self : S.LeftHomologyData) → self.K ⟶ S.X₂the inclusion of cycles in S.X₂
- Cited by
- 144 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 12 definitions · uses no axioms
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.LeftHomologyData.Kstatement · cited by 233
- CategoryTheory.ShortComplex.LeftHomologyDatastatement and proof · cited by 212
Cited by166
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.iCyclesproof · cited by 100
- CategoryTheory.ShortComplex.LeftHomologyData.mapproof · cited by 25
- CategoryTheory.ShortComplex.LeftHomologyData.f'_istatement · cited by 21
- CategoryTheory.ShortComplex.leftRightHomologyComparison'proof · cited by 20
- CategoryTheory.ShortComplex.cyclesMap'_istatement · cited by 18
- CategoryTheory.ShortComplex.LeftHomologyData.opproof · cited by 13
- CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono'proof · cited by 11
- CategoryTheory.ShortComplex.LeftHomologyData.unopproof · cited by 10
- CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMonoproof · cited by 9
- CategoryTheory.ShortComplex.LeftHomologyData.cyclesIso_hom_comp_istatement and proof · cited by 8
- CategoryTheory.ShortComplex.LeftHomologyData.liftK_istatement · cited by 8
- CategoryTheory.ShortComplex.LeftHomologyData.wistatement · cited by 7