Theorems · Theorem · category theory

CategoryTheory.Localization.hasSmallLocalizedHom_iff

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (W : CategoryTheory.MorphismProperty C) {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (L : CategoryTheory.Functor C D) [L.IsLocalization W] {X Y : C},
  CategoryTheory.Localization.HasSmallLocalizedHom W X Y ↔ Small.{w, v₂} (L.obj X ⟶ L.obj Y)

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

6 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization