Theorems · Theorem · category theory

CategoryTheory.Functor.faithful_of_comp_cancel_zero_of_hasLeftCalculusOfFractions

∀ {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] {E : Type u_3}
  [inst_4 : CategoryTheory.Category.{v_3, u_3} E] (F : CategoryTheory.Functor D E) [W.HasLeftCalculusOfFractions]
  [inst_6 : CategoryTheory.Preadditive D] [inst_7 : CategoryTheory.Preadditive E] [L.Additive] [F.Additive],
  (∀ ⦃X₁ X₂ : C⦄ (f : X₁ ⟶ X₂), F.map (L.map f) = 0 → L.map f = 0) → F.Faithful

Defined in

Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive

Cited by

0 results in Mathlib

Foundations

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

Assumes

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