Theorems · Theorem · category theory

CategoryTheory.Localization.homEquiv_eq

∀ {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} (G : CategoryTheory.Functor D₁ D₂)
  (e : L₁.comp G ≅ L₂) (f : L₁.obj X ⟶ L₁.obj Y),
  (CategoryTheory.Localization.homEquiv W L₁ L₂) f =
    CategoryTheory.CategoryStruct.comp (e.inv.app X) (CategoryTheory.CategoryStruct.comp (G.map f) (e.hom.app Y))

Defined in

Mathlib.CategoryTheory.Localization.HomEquiv

Cited by

1 results in Mathlib

Foundations

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

Assumes

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