Theorems · Definition · category theory
CategoryTheory.ShortComplex.RightHomologyData.unop
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex Cᵒᵖ} → S.RightHomologyData → S.unop.LeftHomologyDataA right homology data for a short complex S in the opposite category
induces a left homology data for S.unop.
- Cited by
- 10 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.
Cites17
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 and proof · cited by 8,081
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- Opposite.unopproof · cited by 2,231
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- Quiver.Hom.unopproof · cited by 903
- 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.RightHomologyData.pproof · cited by 84
- CategoryTheory.ShortComplex.RightHomologyData.ιproof · cited by 69
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.HomologyData.unopproof · cited by 6
- CategoryTheory.ShortComplex.RightHomologyMapData.unopstatement · cited by 3
- CategoryTheory.ShortComplex.hasLeftHomology_iff_opproof · cited by 1
- CategoryTheory.ShortComplex.HomologyMapData.unop_leftstatement · cited by 0
- CategoryTheory.ShortComplex.HomologyData.unop_leftstatement · cited by 0
- CategoryTheory.ShortComplex.RightHomologyMapData.unop_φHstatement · cited by 0
- CategoryTheory.ShortComplex.RightHomologyMapData.unop_φKstatement · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.unop_Hstatement and proof · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.unop_Kstatement and proof · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.unop_f'statement · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.unop_istatement and proof · cited by 0
- CategoryTheory.ShortComplex.RightHomologyData.unop_πstatement and proof · cited by 0