Theorems · Theorem · category theory

CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  (S : CategoryTheory.ShortComplex (CochainComplex C ℤ))
  (σ : (n : ℤ) → (S.map (HomologicalComplex.eval C (ComplexShape.up ℤ) n)).Splitting)
  [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C],
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctor (CochainComplex C ℤ) 1).map S.f)
      (CochainComplex.mappingConeHomOfDegreewiseSplitIso S σ).inv =
    -CochainComplex.mappingCone.inr (CochainComplex.homOfDegreewiseSplit S σ)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts