Theorems · Theorem · category theory

CochainComplex.mappingCocone.lift.congr_simp

∀ {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 α_1 : M ⟶ K) (e_α : α = α_1) (β β_1 : CochainComplex.HomComplex.Cochain M L (-1)) (e_β : β = β_1)
  (hαβ :
    CochainComplex.HomComplex.δ (-1) 0 β +
        CochainComplex.HomComplex.Cochain.ofHom (CategoryTheory.CategoryStruct.comp α φ) =
      0),
  CochainComplex.mappingCocone.lift φ α β hαβ = CochainComplex.mappingCocone.lift φ α_1 β_1 ⋯

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber