Theorems · Theorem · category theory

CategoryTheory.Functor.leftDerivedNatTrans_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]
  (LF'' LF' LF : CategoryTheory.Functor D H) {F F' F'' : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D}
  (α'' : L.comp LF'' ⟶ F'') (α' : L.comp LF' ⟶ F') (α : L.comp LF ⟶ F) (W : CategoryTheory.MorphismProperty C)
  [inst_3 : L.IsLocalization W] [inst_4 : LF.IsLeftDerivedFunctor α W] [inst_5 : LF'.IsLeftDerivedFunctor α' W]
  (τ' : F'' ⟶ F') (τ : F' ⟶ F),
  CategoryTheory.CategoryStruct.comp (LF''.leftDerivedNatTrans LF' α'' α' W τ') (LF'.leftDerivedNatTrans LF α' α W τ) =
    LF''.leftDerivedNatTrans LF α'' α W (CategoryTheory.CategoryStruct.comp τ' τ)

Defined in

Mathlib.CategoryTheory.Functor.Derived.LeftDerived

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.IsLeftDerivedFunctorCategoryTheory.Functor.IsLeftDerivedFunctor