Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.isIso_iff_of_hasLeftResolutions

∀ {C₁ : Type u_1} {C₂ : Type u_2} {D₂ : Type u_4} {H : Type u_5} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] [inst_2 : CategoryTheory.Category.{v_4, u_4} D₂]
  [inst_3 : CategoryTheory.Category.{v_5, u_5} H] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂)
  (L₂ : CategoryTheory.Functor C₂ D₂) [L₂.IsLocalization W₂] [Φ.HasLeftResolutions] {F G : CategoryTheory.Functor D₂ H}
  (α : F ⟶ G), CategoryTheory.IsIso α ↔ ∀ (X₁ : C₁), CategoryTheory.IsIso (α.app (L₂.obj (Φ.functor.obj X₁)))

Defined in

Mathlib.CategoryTheory.Localization.Resolution

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.LocalizerMorphism.HasLeftResolutions