Theorems · Definition · category theory

CochainComplex.mappingCone.shiftTrianglehIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] →
        {K L : CochainComplex C ℤ} →
          (φ : K ⟶ L) →
            (n : ℤ) →
              (CategoryTheory.Pretriangulated.Triangle.shiftFunctor (HomotopyCategory C (ComplexShape.up ℤ)) n).obj
                  (CochainComplex.mappingCone.triangleh φ) ≅
                CochainComplex.mappingCone.triangleh ((CategoryTheory.shiftFunctor (CochainComplex C ℤ) n).map φ)

The canonical isomorphism (triangleh φ)⟦n⟧ ≅ triangleh (φ⟦n⟧').

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts