Theorems · Theorem · category theory

CategoryTheory.Localization.SmallHom.equiv_mk

∀ {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}
  [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y] (f : X ⟶ Y),
  (CategoryTheory.Localization.SmallHom.equiv W L) (CategoryTheory.Localization.SmallHom.mk W f) = L.map f

Defined in

Mathlib.CategoryTheory.Localization.SmallHom

Cited by

11 results in Mathlib

Foundations

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

Assumes

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