Theorems · Definition · category theory

CategoryTheory.Localization.SmallHom.chgUniv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {X Y : C} →
        [inst_1 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y] →
          [inst_2 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y] →
            CategoryTheory.Localization.SmallHom W X Y ≃ CategoryTheory.Localization.SmallHom W X Y

Up to an equivalence, the type SmallHom.{w} W X Y n does not depend on the universe w.

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHom