Theorems · Definition · category theory
CategoryTheory.ShortComplex.LeftHomologyData.op
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex C} → S.LeftHomologyData → S.op.RightHomologyDataA left homology data for a short complex S induces a right homology data for S.op.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Oppositestatement · cited by 8,081
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.LeftHomologyData.Hproof · cited by 236
- CategoryTheory.ShortComplex.LeftHomologyData.Kproof · cited by 233
- CategoryTheory.ShortComplex.LeftHomologyDatastatement and proof · cited by 212
- CategoryTheory.ShortComplex.RightHomologyDatastatement · cited by 211
- CategoryTheory.ShortComplex.LeftHomologyData.iproof · cited by 144
- CategoryTheory.ShortComplex.LeftHomologyData.πproof · cited by 106
- CategoryTheory.ShortComplex.opstatement · cited by 88
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.opcyclesOpIsoproof · cited by 8
- CategoryTheory.ShortComplex.HomologyData.opproof · cited by 7
- CategoryTheory.ShortComplex.LeftHomologyMapData.opstatement · cited by 4
- CategoryTheory.ShortComplex.rightHomologyOpIsoproof · cited by 3
- CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_opproof · cited by 2
- CategoryTheory.ShortComplex.op_pOpcycles_opcyclesOpIso_homproof · cited by 2
- CategoryTheory.ShortComplex.LeftHomologyMapData.op_φHstatement · cited by 1
- CategoryTheory.ShortComplex.leftHomologyMap'_opstatement · cited by 1
- CategoryTheory.ShortComplex.LeftHomologyData.op_pstatement and proof · cited by 1
- CategoryTheory.ShortComplex.LeftHomologyMapData.op_φQstatement · cited by 0
- CategoryTheory.ShortComplex.HomologyMapData.op_rightstatement · cited by 0
- CategoryTheory.ShortComplex.HomologyData.op_rightstatement · cited by 0