Theorems · Theorem · category theory

CategoryTheory.Localization.Preadditive.add_eq_add

∀ {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 : C} {X' Y' : D} (eX : L.obj X ≅ X') (eY : L.obj Y ≅ Y') {X'' Y'' : C}
  (eX' : L.obj X'' ≅ X') (eY' : L.obj Y'' ≅ Y') (f₁ f₂ : X' ⟶ Y'),
  CategoryTheory.Localization.Preadditive.add W eX eY f₁ f₂ =
    CategoryTheory.Localization.Preadditive.add W eX' eY' f₁ f₂

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive

Cited by

1 results in Mathlib

Foundations

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

Assumes

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