Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.isLeftDerivabilityStructure_iff

∀ {C₁ : Type u₁} {C₂ : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) {D₁ : Type u_1} {D₂ : Type u_2}
  [inst_2 : CategoryTheory.Category.{v_1, u_1} D₁] [inst_3 : CategoryTheory.Category.{v_2, u_2} D₂]
  (L₁ : CategoryTheory.Functor C₁ D₁) (L₂ : CategoryTheory.Functor C₂ D₂) [L₁.IsLocalization W₁] [L₂.IsLocalization W₂]
  (F : CategoryTheory.Functor D₁ D₂) [Φ.HasLeftResolutions] (e : Φ.functor.comp L₂ ≅ L₁.comp F),
  Φ.IsLeftDerivabilityStructure ↔ CategoryTheory.TwoSquare.GuitartExact e.inv

Defined in

Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic

Cited by

3 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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