Theorems · Definition · category theory
CategoryTheory.ShortComplex.RightHomologyData.op
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex C} → S.RightHomologyData → S.op.LeftHomologyDataA right homology data for a short complex S induces a left homology data for S.op.
- Cited by
- 17 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.LeftHomologyDatastatement · cited by 212
- CategoryTheory.ShortComplex.RightHomologyDatastatement and proof · cited by 211
- CategoryTheory.ShortComplex.RightHomologyData.Qproof · cited by 163
- CategoryTheory.ShortComplex.RightHomologyData.Hproof · cited by 158
- CategoryTheory.ShortComplex.opstatement · cited by 88
- CategoryTheory.ShortComplex.RightHomologyData.pproof · cited by 84
- CategoryTheory.ShortComplex.RightHomologyData.ιproof · cited by 69
Cited by23
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMonoproof · cited by 9
- CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono'proof · cited by 9
- CategoryTheory.ShortComplex.cyclesOpIsoproof · cited by 8
- CategoryTheory.ShortComplex.HomologyData.opproof · cited by 7
- CategoryTheory.ShortComplex.leftHomologyOpIsoproof · cited by 4
- CategoryTheory.ShortComplex.RightHomologyMapData.opstatement · cited by 4
- CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCyclesproof · cited by 2
- CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_invproof · cited by 2
- CategoryTheory.ShortComplex.homologyMap_opproof · cited by 2
- CategoryTheory.ShortComplex.rightHomologyMap'_opstatement · cited by 2
- CategoryTheory.ShortComplex.RightHomologyData.op_istatement and proof · cited by 1
- CategoryTheory.ShortComplex.RightHomologyMapData.op_φHstatement · cited by 1