Theorems · Theorem · category theory

CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v

∀ {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) (p : ℤ),
  (↑(CochainComplex.cocycleOfDegreewiseSplit (CochainComplex.mappingCone.triangleRotateShortComplex φ)
            (CochainComplex.mappingCone.triangleRotateShortComplexSplitting φ))).v
      p (p + 1) ⋯ =
    -φ.f (p + { as := 1 }.as)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts