Theorems · Theorem · category theory

CochainComplex.mappingCocone.lift_f_fst_f_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {K L : CochainComplex C ℤ} (φ : K ⟶ L) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] {M : CochainComplex C ℤ}
  (α : M ⟶ K) (β : CochainComplex.HomComplex.Cochain M L (-1))
  (hαβ :
    CochainComplex.HomComplex.δ (-1) 0 β +
        CochainComplex.HomComplex.Cochain.ofHom (CategoryTheory.CategoryStruct.comp α φ) =
      0)
  (p : ℤ) {Z : C} (h : K.X p ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCocone.lift φ α β hαβ).f p)
      (CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCocone.fst φ).f p) h) =
    CategoryTheory.CategoryStruct.comp (α.f p) h

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber