Theorems · Theorem · category theory

CategoryTheory.LocalizerMorphism.homMap_comp

∀ {C₁ : Type u_2} {C₂ : Type u_3} {D₁ : Type u_5} {D₂ : Type u_6} [inst : CategoryTheory.Category.{v_2, u_2} C₁]
  [inst_1 : CategoryTheory.Category.{v_3, u_3} C₂] [inst_2 : CategoryTheory.Category.{v_5, u_5} D₁]
  [inst_3 : CategoryTheory.Category.{v_6, u_6} D₂] {W₁ : CategoryTheory.MorphismProperty C₁}
  {W₂ : CategoryTheory.MorphismProperty C₂} (Φ : CategoryTheory.LocalizerMorphism W₁ W₂)
  (L₁ : CategoryTheory.Functor C₁ D₁) [inst_4 : L₁.IsLocalization W₁] (L₂ : CategoryTheory.Functor C₂ D₂)
  [inst_5 : L₂.IsLocalization W₂] {X Y Z : C₁} (f : L₁.obj X ⟶ L₁.obj Y) (g : L₁.obj Y ⟶ L₁.obj Z),
  Φ.homMap L₁ L₂ (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (Φ.homMap L₁ L₂ f) (Φ.homMap L₁ L₂ g)

Defined in

Mathlib.CategoryTheory.Localization.HomEquiv

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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