Theorems · Theorem · category theory

CategoryTheory.Localization.homEquiv_id

∀ {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 : C),
  (CategoryTheory.Localization.homEquiv W L₁ L₂) (CategoryTheory.CategoryStruct.id (L₁.obj X)) =
    CategoryTheory.CategoryStruct.id (L₂.obj X)

Defined in

Mathlib.CategoryTheory.Localization.HomEquiv

Cited by

2 results in Mathlib

Foundations

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

Assumes

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