Theorems · Definition · category theory
CategoryTheory.Pretriangulated.rotate
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.Preadditive C] →
[inst_2 : CategoryTheory.HasShift C ℤ] →
CategoryTheory.Functor (CategoryTheory.Pretriangulated.Triangle C) (CategoryTheory.Pretriangulated.Triangle C)Rotating triangles gives an endofunctor on the category of triangles in C.
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 43 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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.shiftFunctorproof · cited by 1,553
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
- CategoryTheory.Pretriangulated.Trianglestatement and proof · cited by 645
- CategoryTheory.Pretriangulated.TriangleMorphism.hom₁proof · cited by 111
- CategoryTheory.Pretriangulated.TriangleMorphism.hom₂proof · cited by 110
- CategoryTheory.Pretriangulated.TriangleMorphism.hom₃proof · cited by 106
- CategoryTheory.Pretriangulated.Triangle.rotateproof · cited by 43
Cited by38
Results whose statement or proof uses this declaration.
- CategoryTheory.Pretriangulated.invRotCompRotstatement and proof · cited by 9
- CategoryTheory.Pretriangulated.rotCompInvRotstatement and proof · cited by 8
- CategoryTheory.Functor.mapTriangleRotateIsostatement and proof · cited by 8
- CategoryTheory.Pretriangulated.triangleRotationproof · cited by 7
- HomotopyCategory.Pretriangulated.rotate_distinguished_triangle'proof · cited by 2
- CategoryTheory.Pretriangulated.rotateRotateRotateIsostatement and proof · cited by 1
- CochainComplex.trianglehOfDegreewiseSplitRotateRotateIsoproof · cited by 1
- CategoryTheory.Pretriangulated.invRotateIsoRotateRotateShiftFunctorNegOnestatement and proof · cited by 1
- CategoryTheory.Pretriangulated.isIso₃_of_isIso₁₂proof · cited by 1
- HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplitproof · cited by 0
- CategoryTheory.Pretriangulated.rotCompInvRot.congr_simpstatement · cited by 0
- CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁statement · cited by 0