Theorems · Definition · category theory
CategoryTheory.ShortComplex.HomologyData.unop
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{S : CategoryTheory.ShortComplex Cᵒᵖ} → S.HomologyData → S.unop.HomologyDataA homology data for a short complex S in the opposite category
induces a homology data for S.unop.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 36 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
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.HomologyData.leftproof · cited by 130
- CategoryTheory.ShortComplex.HomologyDatastatement and proof · cited by 102
- CategoryTheory.ShortComplex.HomologyData.rightproof · cited by 99
- CategoryTheory.ShortComplex.HomologyData.isoproof · cited by 45
- CategoryTheory.ShortComplex.unopstatement · cited by 44
- CategoryTheory.Iso.unopproof · cited by 33
- CategoryTheory.ShortComplex.RightHomologyData.unopproof · cited by 10
- CategoryTheory.ShortComplex.LeftHomologyData.unopproof · cited by 10
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.Exact.unopproof · cited by 4
- CategoryTheory.ShortComplex.HomologyMapData.unopstatement · cited by 2
- CategoryTheory.ShortComplex.HomologyMapData.unop_leftstatement · cited by 0
- CategoryTheory.ShortComplex.HomologyMapData.unop_rightstatement · cited by 0
- CategoryTheory.ShortComplex.HomologyData.unop_leftstatement and proof · cited by 0
- CategoryTheory.ShortComplex.HomologyData.unop_rightstatement and proof · cited by 0
- CategoryTheory.ShortComplex.HomologyData.unop_isostatement and proof · cited by 0