Theorems · Definition · category theory
CategoryTheory.ShortComplex.RightHomologyData.canonical
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
(S : CategoryTheory.ShortComplex C) → [S.HasHomology] → S.RightHomologyDataGiven a short complex S such that S.HasHomology, this is the canonical
right homology data for S whose Q and H fields are
respectively S.opcycles and S.homology.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.HasHomologystatement and proof · cited by 253
- CategoryTheory.ShortComplex.homologyproof · cited by 216
- CategoryTheory.ShortComplex.RightHomologyDatastatement · cited by 211
- CategoryTheory.ShortComplex.opcyclesproof · cited by 192
- CategoryTheory.ShortComplex.pOpcyclesproof · cited by 84
- CategoryTheory.ShortComplex.homologyιproof · cited by 51
- CategoryTheory.ShortComplex.homologyι_comp_fromOpcyclesproof · cited by 11
- CategoryTheory.ShortComplex.opcyclesIsCokernelproof · cited by 5
- CategoryTheory.ShortComplex.homologyIsKernelproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.HomologyData.canonicalproof · cited by 10
- HomologicalComplex.truncGE.rightHomologyMapDatastatement and proof · cited by 3
- CategoryTheory.ShortComplex.RightHomologyData.canonical_Hstatement and proof · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.canonical_Qstatement and proof · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.canonical_g'statement · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.canonical_pstatement and proof · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.canonical_ιstatement and proof · cited by 0
- HomologicalComplex.truncGE.rightHomologyMapData_φHstatement · cited by 0
- HomologicalComplex.truncGE.rightHomologyMapData_φQstatement · cited by 0