Theorems · Theorem · category theory

HomotopyCategory.Pretriangulated.shift_distinguished_triangle

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C],
  ∀ T ∈ HomotopyCategory.Pretriangulated.distinguishedTriangles C,
    ∀ (n : ℤ),
      (CategoryTheory.Pretriangulated.Triangle.shiftFunctor (HomotopyCategory C (ComplexShape.up ℤ)) n).obj T ∈
        HomotopyCategory.Pretriangulated.distinguishedTriangles C

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated
Cited by: 1 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasBinaryBiproducts

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Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homproof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functor.mapproof · cited by 8,698
CategoryTheory.Isoproof · cited by 3,963
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.shiftFunctorproof · cited by 1,553
ComplexShape.upstatement and proof · cited by 1,123
CochainComplexproof · cited by 1,016
CategoryTheory.Pretriangulated.Trianglestatement and proof · cited by 645
CategoryTheory.Iso.transproof · cited by 566

Cited by1

Results whose statement or proof uses this declaration.

HomotopyCategory.Pretriangulated.invRotate_distinguished_triangle'proof · cited by 1