Theorems · Theorem · category theory

CategoryTheory.Localization.SmallHom.equiv_mkInv

∀ {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) [inst_2 : L.IsLocalization W] {X Y : C}
  (f : Y ⟶ X) (hf : W f) [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y],
  (CategoryTheory.Localization.SmallHom.equiv W L) (CategoryTheory.Localization.SmallHom.mkInv f hf) =
    (CategoryTheory.Localization.isoOfHom L W f hf).inv

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

4 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Localization.HasSmallLocalizedHom