Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.Derives.isRightDerivedFunctor_iff_isIso

∀ {C₁ : Type u₁} {C₂ : Type u₂} {H : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} H] {D₂ : Type u₄}
  [inst_3 : CategoryTheory.Category.{v₄, u₄} D₂] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} {Φ : CategoryTheory.LocalizerMorphism W₁ W₂}
  {F : CategoryTheory.Functor C₂ H},
  Φ.Derives F →
    ∀ [Φ.IsRightDerivabilityStructure] {L₂ : CategoryTheory.Functor C₂ D₂} [inst_5 : L₂.IsLocalization W₂]
      {RF : CategoryTheory.Functor D₂ H} (α : F ⟶ L₂.comp RF),
      RF.IsRightDerivedFunctor α W₂ ↔ ∀ (X₁ : C₁), CategoryTheory.IsIso (α.app (Φ.functor.obj X₁))

Defined in

Mathlib.CategoryTheory.Localization.DerivabilityStructure.Derives

Cited by

0 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.LocalizerMorphism.IsRightDerivabilityStructureCategoryTheory.Functor.IsLocalization