Theorems · Theorem · category theory

HomologicalComplex.homotopyCofiber.mapArrowHom_comp

∀ {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 : HomologicalComplex C c} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ]
  [inst_3 : DecidableRel c.Rel] {F' F'' G' G'' : HomologicalComplex C c} (φ' : F' ⟶ G') (φ'' : F'' ⟶ G'')
  [inst_4 : HomologicalComplex.HasHomotopyCofiber φ'] [inst_5 : HomologicalComplex.HasHomotopyCofiber φ'']
  (H : ∀ (j : ι), ∃ i, c.Rel i j) (α : CategoryTheory.Arrow.mk φ ⟶ CategoryTheory.Arrow.mk φ')
  (β : CategoryTheory.Arrow.mk φ' ⟶ CategoryTheory.Arrow.mk φ''),
  HomologicalComplex.homotopyCofiber.mapArrowHom φ φ'' H (CategoryTheory.CategoryStruct.comp α β) =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.mapArrowHom φ φ' H α)
      (HomologicalComplex.homotopyCofiber.mapArrowHom φ' φ'' H β)

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

1 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRelHomologicalComplex.HasHomotopyCofiberHomologicalComplex.HasHomotopyCofiber