Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.SerreClassLocalization.epi_map_tfae

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {D : Type u'}
  [inst_2 : CategoryTheory.Category.{v', u'} D] (L : CategoryTheory.Functor C D) (P : CategoryTheory.ObjectProperty C)
  [inst_3 : P.IsSerreClass] [L.IsLocalization P.isoModSerre] [inst_5 : CategoryTheory.Preadditive D] [L.Additive]
  {X Y : C} (f : X ⟶ Y),
  [CategoryTheory.Epi (L.map f), P.epiModSerre f,
      ∀ ⦃Z : C⦄ (z : Y ⟶ Z), CategoryTheory.CategoryStruct.comp (L.map f) (L.map z) = 0 → L.map z = 0].TFAE

Defined in

Mathlib.CategoryTheory.Abelian.SerreClass.Localization

Cited by

1 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.ObjectProperty.IsSerreClassCategoryTheory.Functor.IsLocalizationCategoryTheory.PreadditiveCategoryTheory.Functor.Additive