Theorems · Theorem · category theory

CochainComplex.mappingCone.inl_fst_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] {K : CochainComplex C ℤ}
  {d e : ℤ} (γ : CochainComplex.HomComplex.Cochain F K d) (he : 1 + d = e),
  (CochainComplex.mappingCone.inl φ).comp ((↑(CochainComplex.mappingCone.fst φ)).comp γ he) ⋯ = γ

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

3 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber