Theorems · Theorem · category theory

DerivedCategory.mappingCocone_triangle_distinguished

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : HasDerivedCategory C] {K L : CochainComplex C ℤ} (φ : K ⟶ L),
  DerivedCategory.Q.mapTriangle.obj (CochainComplex.mappingCocone.triangle φ) ∈
    CategoryTheory.Pretriangulated.distinguishedTriangles

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian HasDerivedCategory

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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.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
CategoryTheory.Iso.transproof · cited by 566
CategoryTheory.Pretriangulated.distinguishedTrianglesstatement · cited by 316
CategoryTheory.Iso.appproof · cited by 253
CategoryTheory.Functor.mapIsoproof · cited by 224

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