Theorems · Theorem · category theory

HomologicalComplex.homotopyCofiber.inr_desc_assoc

∀ {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] (α : G ⟶ K) (hα : Homotopy (CategoryTheory.CategoryStruct.comp φ α) 0)
  {Z : HomologicalComplex C c} (h : K ⟶ Z),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.inr φ)
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.desc φ α hα) h) =
    CategoryTheory.CategoryStruct.comp α h

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRel