Theorems · Theorem · category theory

CategoryTheory.NatTrans.leftDerivedToHomotopyCategory_comp_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u_1} [inst_1 : CategoryTheory.Category.{v_1, u_1} D]
  [inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.HasProjectiveResolutions C]
  [inst_4 : CategoryTheory.Abelian D] {F G H : CategoryTheory.Functor C D} (α : F ⟶ G) (β : G ⟶ H) [inst_5 : F.Additive]
  [inst_6 : G.Additive] [inst_7 : H.Additive] {Z : CategoryTheory.Functor C (HomotopyCategory D (ComplexShape.down ℕ))}
  (h : H.leftDerivedToHomotopyCategory ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.NatTrans.leftDerivedToHomotopyCategory (CategoryTheory.CategoryStruct.comp α β)) h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.NatTrans.leftDerivedToHomotopyCategory α)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.NatTrans.leftDerivedToHomotopyCategory β) h)

Defined in

Mathlib.CategoryTheory.Abelian.LeftDerived

Cited by

0 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasProjectiveResolutionsCategoryTheory.AbelianCategoryTheory.Functor.AdditiveCategoryTheory.Functor.AdditiveCategoryTheory.Functor.Additive