Theorems · Theorem · category theory

CategoryTheory.Localization.homEquiv_trans

∀ {C : Type u_1} {D₁ : Type u_5} {D₂ : Type u_6} {D₃ : Type u_7} [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]
  [inst_3 : CategoryTheory.Category.{v_7, u_7} D₃] (W : CategoryTheory.MorphismProperty C)
  (L₁ : CategoryTheory.Functor C D₁) [inst_4 : L₁.IsLocalization W] (L₂ : CategoryTheory.Functor C D₂)
  [inst_5 : L₂.IsLocalization W] (L₃ : CategoryTheory.Functor C D₃) [inst_6 : L₃.IsLocalization W] {X Y : C}
  (f : L₁.obj X ⟶ L₁.obj Y),
  (CategoryTheory.Localization.homEquiv W L₂ L₃) ((CategoryTheory.Localization.homEquiv W L₁ L₂) f) =
    (CategoryTheory.Localization.homEquiv W L₁ L₃) f

Defined in

Mathlib.CategoryTheory.Localization.HomEquiv

Cited by

1 results in Mathlib

Foundations

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

Assumes

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