Theorems · Theorem · category theory

CategoryTheory.Localization.functor_additive_iff

∀ {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) [L.IsLocalization W]
  [W.HasLeftCalculusOfFractions] {E : Type u_3} [inst_5 : CategoryTheory.Category.{v_3, u_3} E]
  [inst_6 : CategoryTheory.Preadditive E] [inst_7 : CategoryTheory.Preadditive D] [L.Additive]
  (G : CategoryTheory.Functor D E), G.Additive ↔ (L.comp G).Additive

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Functor.IsLocalizationCategoryTheory.MorphismProperty.HasLeftCalculusOfFractionsCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.Functor.Additive