Theorems · Inductive type · category theory
CategoryTheory.ShortComplex.HasHomology
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → CategoryTheory.ShortComplex C → PropA short complex S has homology when there exists a S.HomologyData
- Cited by
- 253 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 by292
Results whose statement or proof uses this declaration.
- HomologicalComplex.HasHomologyproof · cited by 342
- CategoryTheory.ShortComplex.homologystatement and proof · cited by 216
- CategoryTheory.ShortComplex.homologyMapstatement and proof · cited by 83
- CategoryTheory.ShortComplex.homologyπstatement and proof · cited by 71
- CategoryTheory.ShortComplex.homologyιstatement and proof · cited by 51
- CategoryTheory.ShortComplex.QuasiIsostatement · cited by 35
- CategoryTheory.ShortComplex.LeftHomologyData.homologyIsostatement and proof · cited by 34
- CategoryTheory.ShortComplex.homologyDatastatement and proof · cited by 33
- CategoryTheory.ShortComplex.leftHomologyIsostatement and proof · cited by 27
- CategoryTheory.ShortComplex.RightHomologyData.homologyIsostatement and proof · cited by 27
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelstatement and proof · cited by 25
- CategoryTheory.ShortComplex.exact_of_f_is_kernelstatement and proof · cited by 22
Showing the 200 most cited of 292.