Theorems · Inductive type · category theory

CategoryTheory.LocalizerMorphism.IsLeftDerivabilityStructure

{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} → CategoryTheory.LocalizerMorphism W₁ W₂ → Prop

A localizer morphism Φ : LocalizerMorphism W₁ W₂ is a left derivability structure if it has left resolutions and the 2-square where the top and bottom functors are localization functors for W₁ and W₂ is Guitart exact.

Defined in

Mathlib.CategoryTheory.Localization.DerivabilityStructure.Basic

Cited by

9 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category