Theorems · Theorem · category theory

CategoryTheory.Functor.leftDerivedNatTrans_app_assoc

∀ {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 : CategoryTheory.Functor D H) {F F' : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D}
  (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] (τ : F' ⟶ F) (X : C) {Z : H} (h : F.obj X ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((LF'.leftDerivedNatTrans LF α' α W τ).app (L.obj X))
      (CategoryTheory.CategoryStruct.comp (α.app X) h) =
    CategoryTheory.CategoryStruct.comp (α'.app X) (CategoryTheory.CategoryStruct.comp (τ.app X) h)

Defined in

Mathlib.CategoryTheory.Functor.Derived.LeftDerived

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsLeftDerivedFunctor