Theorems · Theorem · category theory

HomologicalComplex.homotopyCofiber.eq_desc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {ι : Type u_2}
  {c : ComplexShape ι} {F G K : HomologicalComplex C c} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ]
  [inst_3 : DecidableRel c.Rel] (f : HomologicalComplex.homotopyCofiber φ ⟶ K) (hc : ∀ (j : ι), ∃ i, c.Rel i j),
  f =
    HomologicalComplex.homotopyCofiber.desc φ
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.inr φ) f)
      ((Homotopy.ofEq ⋯).trans
        (((HomologicalComplex.homotopyCofiber.inrCompHomotopy φ hc).compRight f).trans (Homotopy.ofEq ⋯)))

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

0 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRel