Theorems · Definition · category theory

CategoryTheory.Localization.Preadditive.addCommGroup

{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' : D) → AddCommGroup (X' ⟶ Y')

The abelian group structure on 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

2 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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