Theorems · Definition · category theory
CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.HasShift C ℤ] →
CategoryTheory.Functor (CategoryTheory.Pretriangulated.Triangle C)ᵒᵖ (CategoryTheory.Pretriangulated.Triangle Cᵒᵖ)The functor which sends a triangle X ⟶ Y ⟶ Z ⟶ X⟦1⟧ in C to the triangle
op Z ⟶ op Y ⟶ op X ⟶ (op Z)⟦1⟧ in Cᵒᵖ (without introducing signs).
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Iso.invproof · cited by 6,514
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.opproof · cited by 1,948
- CategoryTheory.shiftFunctorproof · cited by 1,553
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.Pretriangulated.triangleOpEquivalenceproof · cited by 34
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIsostatement and proof · cited by 7
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIsostatement and proof · cited by 3
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_appstatement · cited by 0
- CategoryTheory.Pretriangulated.triangleOpEquivalence_counitIsostatement · cited by 0
- CategoryTheory.Pretriangulated.triangleOpEquivalence_functorstatement · cited by 0
- CategoryTheory.Pretriangulated.triangleOpEquivalence_unitIsostatement · cited by 0
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₁statement · cited by 0
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₂statement · cited by 0
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_hom_app_hom₃statement · cited by 0
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁statement · cited by 0
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₂statement · cited by 0