Theorems · Theorem · category theory

CategoryTheory.Localization.Preadditive.add_comp_assoc

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Preadditive C]
  {L : CategoryTheory.Functor C D} (W : CategoryTheory.MorphismProperty C) [inst_3 : L.IsLocalization W]
  [inst_4 : W.HasLeftCalculusOfFractions] {X Y Z : C} {X' Y' Z' : D} (eX : L.obj X ≅ X') (eY : L.obj Y ≅ Y')
  (eZ : L.obj Z ≅ Z') (f₁ f₂ : X' ⟶ Y') (g : Y' ⟶ Z') {Z_1 : D} (h : Z' ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Localization.Preadditive.add W eX eY f₁ f₂)
      (CategoryTheory.CategoryStruct.comp g h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Localization.Preadditive.add W eX eZ (CategoryTheory.CategoryStruct.comp f₁ g)
        (CategoryTheory.CategoryStruct.comp f₂ g))
      h

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Functor.IsLocalizationCategoryTheory.MorphismProperty.HasLeftCalculusOfFractions