Theorems · Definition · category theory

CategoryTheory.Localization.Preadditive.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] →
        [CategoryTheory.Preadditive C] →
          {L : CategoryTheory.Functor C D} →
            (W : CategoryTheory.MorphismProperty C) →
              [L.IsLocalization W] →
                [W.HasLeftCalculusOfFractions] →
                  {X Y : C} → {X' Y' : D} → (L.obj X ≅ X') → (L.obj Y ≅ Y') → (X' ⟶ Y') → (X' ⟶ Y') → (X' ⟶ Y')

The addition of morphisms in D, when L : C ⥤ D is a localization functor, C is preadditive and there is a left calculus of fractions.

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive

Cited by

7 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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