Theorems · Theorem · category theory

CochainComplex.mappingCone.id_X

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G : CochainComplex C ℤ} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] (p q : ℤ) (hpq : p + 1 = q),
  CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCone.fst φ)).v p q hpq)
        ((CochainComplex.mappingCone.inl φ).v q p ⋯) +
      CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.snd φ).v p p ⋯)
        ((CochainComplex.mappingCone.inr φ).f p) =
    CategoryTheory.CategoryStruct.id ((CochainComplex.mappingCone φ).X p)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber