Theorems · Definition · category theory
CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] →
[inst_2 : CategoryTheory.HasShift C ℤ] →
CategoryTheory.Pretriangulated.Triangle.shiftFunctor C 0 ≅
CategoryTheory.Functor.id (CategoryTheory.Pretriangulated.Triangle C)The canonical isomorphism Triangle.shiftFunctor C 0 ≅ 𝟭 (Triangle C).
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.Functorstatement · cited by 16,252
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement and proof · cited by 3,333
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
- CategoryTheory.Pretriangulated.Trianglestatement and proof · cited by 645
- CategoryTheory.Pretriangulated.Triangle.obj₁proof · cited by 360
- CategoryTheory.Pretriangulated.Triangle.obj₃proof · cited by 332
- CategoryTheory.Pretriangulated.Triangle.obj₂proof · cited by 316
- CategoryTheory.Iso.appproof · cited by 253
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Pretriangulated.Triangle.shift_distinguishedproof · cited by 4
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorAdd_eqproof · cited by 1
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_eqstatement and proof · cited by 0
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₁statement and proof · cited by 0
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₂statement and proof · cited by 0
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_hom_app_hom₃statement and proof · cited by 0
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁statement and proof · cited by 0
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₂statement and proof · cited by 0
- CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₃statement and proof · cited by 0