Theorems · Theorem · category theory

CategoryTheory.Functor.isLeftDerivedFunctor_iff_isIso_leftDerivedLift

∀ {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]
  (LF : CategoryTheory.Functor D H) {F : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D}
  (α : L.comp LF ⟶ F) (W : CategoryTheory.MorphismProperty C) [inst_3 : L.IsLocalization W]
  [inst_4 : LF.IsLeftDerivedFunctor α W] (G : CategoryTheory.Functor D H) (β : L.comp G ⟶ F),
  G.IsLeftDerivedFunctor β W ↔ CategoryTheory.IsIso (LF.leftDerivedLift α W G β)

Defined in

Mathlib.CategoryTheory.Functor.Derived.LeftDerived

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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