Theorems · Definition · category theory

CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution

{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) →
                    [L.IsLocalization W₂] →
                      {X₂ : C₂} →
                        {X₃ : D} →
                          (y : L.obj X₂ ⟶ X₃) →
                            CategoryTheory.Functor (Φ.RightResolution X₂)
                              ((CategoryTheory.TwoSquare.mk Φ.functor (Φ.functor.comp L) L (CategoryTheory.Functor.id D)
                                    (Φ.functor.comp L).rightUnitor.inv).CostructuredArrowDownwards
                                y)

Given Φ : LocalizerMorphism W₁ W₂, L : C₂ ⥤ D a localization functor for W₂ and a morphism y : L.obj X₂ ⟶ X₃, this is the functor which sends R : Φ.RightResolution d to (isoOfHom L W₂ R.w R.hw).inv ≫ y in the category w.CostructuredArrowDownwards y where w is TwoSquare.mk Φ.functor (Φ.functor ⋙ L) L (𝟭 _) (Functor.rightUnitor _).inv.

Defined in

Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor

Cited by

4 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization