Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.binaryProductTriangle_distinguished

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroObject C]
  [inst_2 : CategoryTheory.HasShift C ℤ] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [hC : CategoryTheory.Pretriangulated C] (X₁ X₂ : C),
  CategoryTheory.Pretriangulated.binaryProductTriangle X₁ X₂ ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

Defined in: Mathlib.CategoryTheory.Triangulated.Pretriangulated
Cited by: 0 results in Mathlib
Foundations: Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroObject CategoryTheory.HasShift CategoryTheory.Preadditive CategoryTheory.Functor.Additive CategoryTheory.Pretriangulated

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Setstatement · cited by 53,352
CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
CategoryTheory.HasShiftstatement and proof · cited by 1,527
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
CategoryTheory.Pretriangulatedstatement and proof · cited by 669
CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
CategoryTheory.Pretriangulated.distinguishedTrianglesstatement · cited by 316
CategoryTheory.Pretriangulated.isomorphic_distinguishedproof · cited by 47
CategoryTheory.Pretriangulated.binaryBiproductTriangleproof · cited by 14

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