Theorems · Theorem · category theory
HomotopyCategory.Pretriangulated.rotate_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 : CategoryTheory.Pretriangulated.Triangle (HomotopyCategory C (ComplexShape.up ℤ))),
T ∈ HomotopyCategory.Pretriangulated.distinguishedTriangles C ↔
T.rotate ∈ HomotopyCategory.Pretriangulated.distinguishedTriangles C- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- ComplexShape.upstatement and proof · cited by 1,123
- CategoryTheory.Pretriangulated.Trianglestatement and proof · cited by 645
- CategoryTheory.Equivalence.unitIsoproof · cited by 536
- CategoryTheory.Iso.appproof · cited by 253
- CategoryTheory.Limits.HasBinaryBiproductsstatement and proof · cited by 165
- HomotopyCategorystatement and proof · cited by 132
- CategoryTheory.Pretriangulated.Triangle.rotatestatement and proof · cited by 43
- CategoryTheory.Pretriangulated.Triangle.invRotateproof · cited by 38
- HomotopyCategory.Pretriangulated.distinguishedTrianglesstatement and proof · cited by 8
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