Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map

∀ {C₁ : Type u_1} {C₂ : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C₁]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂) {D : Type u_3}
  [inst_2 : CategoryTheory.Category.{v_3, u_3} D] (L : CategoryTheory.Functor C₂ D) [inst_3 : L.IsLocalization W₂]
  {X₂ : C₂} {X₃ : D} (y : L.obj X₂ ⟶ X₃) {R R' : Φ.RightResolution X₂} (φ : R ⟶ R'),
  (CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution Φ L y).map φ =
    CategoryTheory.CostructuredArrow.homMk (CategoryTheory.StructuredArrow.homMk φ.f ⋯) ⋯

Defined in

Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization