Theorems · Definition · category theory
CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.HasShift C ℤ] →
CategoryTheory.Functor.id (CategoryTheory.Pretriangulated.Triangle C)ᵒᵖ ≅
(CategoryTheory.Pretriangulated.TriangleOpEquivalence.functor C).comp
(CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse C)The unit isomorphism of the
equivalence triangleOpEquivalence C : (Triangle C)ᵒᵖ ≌ Triangle Cᵒᵖ .
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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
- CategoryTheory.Functor.objproof · cited by 19,642
- 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.Functor.compstatement · cited by 6,529
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement · cited by 3,333
- Opposite.unopproof · cited by 2,231
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Pretriangulated.triangleOpEquivalenceproof · cited by 34
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_inv_appstatement and proof · cited by 0
- CategoryTheory.Pretriangulated.triangleOpEquivalence_unitIsostatement · cited by 0
- CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso_hom_appstatement and proof · cited by 0