Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.SerreClassLocalization.map_comp_eq_zero_iff_of_epi_mono

∀ {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 Z Y : C} (f : X ⟶ Z) (g : Z ⟶ Y) [CategoryTheory.Epi f] [CategoryTheory.Mono g],
  CategoryTheory.CategoryStruct.comp (L.map f) (L.map g) = 0 ↔ P Z

Defined in

Mathlib.CategoryTheory.Abelian.SerreClass.Localization

Cited by

2 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.ObjectProperty.IsSerreClassCategoryTheory.Functor.IsLocalizationCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.EpiCategoryTheory.Mono