Theorems · Theorem · category theory

CochainComplex.mappingCone.d_fst_v_assoc

∀ {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] (i j k : ℤ)
  (hij : i + 1 = j) (hjk : j + 1 = k) {Z : C} (h : F.X k ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone φ).d i j)
      (CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCone.fst φ)).v j k hjk) h) =
    CategoryTheory.CategoryStruct.comp
      (-CategoryTheory.CategoryStruct.comp ((↑(CochainComplex.mappingCone.fst φ)).v i j hij) (F.d j k)) h

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

0 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber