Theorems · Theorem · category theory

CategoryTheory.Functor.rightDerived_fac_app

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

Defined in

Mathlib.CategoryTheory.Functor.Derived.RightDerived

Cited by

3 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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