Theorems · Definition · category theory
CategoryTheory.ShortComplex.op
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
CategoryTheory.ShortComplex C → CategoryTheory.ShortComplex CᵒᵖThe opposite ShortComplex in Cᵒᵖ associated to a short complex in C.
- Cited by
- 88 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.gproof · cited by 658
- CategoryTheory.ShortComplex.fproof · cited by 653
Cited by107
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.opMapstatement · cited by 42
- CategoryTheory.ShortComplex.RightHomologyData.opstatement · cited by 17
- CategoryTheory.ShortComplex.LeftHomologyData.opstatement · cited by 13
- CategoryTheory.ShortComplex.SnakeInput.opproof · cited by 10
- CategoryTheory.ShortComplex.opFunctorproof · cited by 8
- CategoryTheory.ShortComplex.opcyclesOpIsostatement · cited by 8
- CategoryTheory.ShortComplex.cyclesOpIsostatement · cited by 8
- CategoryTheory.ShortComplex.HomologyData.opstatement · cited by 7
- CategoryTheory.ShortComplex.Exact.opstatement · cited by 5
- CategoryTheory.ShortComplex.homologyOpIsostatement and proof · cited by 5
- CategoryTheory.ShortComplex.HomologyMapData.opstatement · cited by 4
- CategoryTheory.ShortComplex.Homotopy.opstatement · cited by 4