Theorems · Theorem · category theory

CategoryTheory.Localization.homEquiv_isoOfHom_inv

∀ {C : Type u_1} {D₁ : Type u_5} {D₂ : Type u_6} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_5, u_5} D₁] [inst_2 : CategoryTheory.Category.{v_6, u_6} D₂]
  (W : CategoryTheory.MorphismProperty C) (L₁ : CategoryTheory.Functor C D₁) [inst_3 : L₁.IsLocalization W]
  (L₂ : CategoryTheory.Functor C D₂) [inst_4 : L₂.IsLocalization W] {X Y : C} (f : Y ⟶ X) (hf : W f),
  (CategoryTheory.Localization.homEquiv W L₁ L₂) (CategoryTheory.Localization.isoOfHom L₁ W f hf).inv =
    (CategoryTheory.Localization.isoOfHom L₂ W f hf).inv

Defined in

Mathlib.CategoryTheory.Localization.HomEquiv

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsLocalization