Theorems · Definition · category theory

CochainComplex.mappingCone.triangleRotateIsoTriangleOfDegreewiseSplit

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] →
        {K L : CochainComplex C ℤ} →
          (φ : K ⟶ L) →
            (CochainComplex.mappingCone.triangle φ).rotate ≅
              CochainComplex.triangleOfDegreewiseSplit (CochainComplex.mappingCone.triangleRotateShortComplex φ)
                (CochainComplex.mappingCone.triangleRotateShortComplexSplitting φ)

The triangle (triangle φ).rotate is isomorphic to a triangle attached to a degreewise split short exact sequence of cochain complexes.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts