Theorems · Definition · category theory

CategoryTheory.Localization.isoOfHom

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        (L : CategoryTheory.Functor C D) →
          (W : CategoryTheory.MorphismProperty C) →
            [L.IsLocalization W] → {X Y : C} → (f : X ⟶ Y) → W f → (L.obj X ≅ L.obj Y)

The isomorphism L.obj X ≅ L.obj Y that is deduced from a morphism f : X ⟶ Y which belongs to W, when L.IsLocalization W.

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

35 results in Mathlib

Foundations

Depth 11 from the axioms · uses Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization