Theorems · Theorem · category theory

CategoryTheory.Functor.rightDerivedNatTrans_comp

∀ {C : Type u_1} {D : Type u_3} {H : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_3} D] [inst_2 : CategoryTheory.Category.{v_5, u_2} H]
  (RF RF' RF'' : CategoryTheory.Functor D H) {F F' F'' : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D}
  (α : F ⟶ L.comp RF) (α' : F' ⟶ L.comp RF') (α'' : F'' ⟶ L.comp RF'') (W : CategoryTheory.MorphismProperty C)
  [inst_3 : L.IsLocalization W] [inst_4 : RF.IsRightDerivedFunctor α W] [inst_5 : RF'.IsRightDerivedFunctor α' W]
  (τ : F ⟶ F') (τ' : F' ⟶ F''),
  CategoryTheory.CategoryStruct.comp (RF.rightDerivedNatTrans RF' α α' W τ)
      (RF'.rightDerivedNatTrans RF'' α' α'' W τ') =
    RF.rightDerivedNatTrans RF'' α α'' W (CategoryTheory.CategoryStruct.comp τ τ')

Defined in

Mathlib.CategoryTheory.Functor.Derived.RightDerived

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsRightDerivedFunctorCategoryTheory.Functor.IsRightDerivedFunctor