Theorems · Definition · category theory
HomologicalComplex.HasHomology
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{ι : Type u_2} → {c : ComplexShape ι} → HomologicalComplex C c → ι → PropA homological complex K has homology in degree i if the associated
short complex K.sc i has.
- Cited by
- 342 results in Mathlib
- Foundations
- Depth 23 from the axioms, rests on 134 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.ShortComplex.HasHomologyproof · cited by 253
- HomologicalComplex.scproof · cited by 205
Cited by448
Results whose statement or proof uses this declaration.
- HomologicalComplex.homologystatement and proof · cited by 209
- HomologicalComplex.cyclesstatement and proof · cited by 164
- HomologicalComplex.opcyclesstatement and proof · cited by 153
- HomologicalComplex.homologyMapstatement and proof · cited by 102
- HomologicalComplex.iCyclesstatement and proof · cited by 80
- HomologicalComplex.pOpcyclesstatement and proof · cited by 71
- HomologicalComplex.homologyπstatement and proof · cited by 69
- HomologicalComplex.cyclesMapstatement and proof · cited by 59
- QuasiIsoAtstatement · cited by 55
- QuasiIsostatement · cited by 52
- HomologicalComplex.homologyιstatement and proof · cited by 48
- HomologicalComplex.opcyclesMapstatement and proof · cited by 47
Showing the 200 most cited of 448.