Theorems · Definition · category theory

CategoryTheory.ObjectProperty.SerreClassLocalization.fullyFaithfulWhiskeringLeft

{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] →
                (E : Type u'') →
                  [inst_4 : CategoryTheory.Category.{v'', u''} E] →
                    [inst_5 : CategoryTheory.Abelian E] →
                      [inst_6 : L.IsLocalization P.isoModSerre] →
                        [inst_7 : CategoryTheory.Preadditive D] →
                          [inst_8 : L.Additive] →
                            (CategoryTheory.ObjectProperty.SerreClassLocalization.whiskeringLeft L P E).FullyFaithful

When L : C ⥤ D is a localization functor with respect to a Serre class in the abelian category C, the functor whiskeringLeft L P E: (D ⥤ₑ E) ⥤ C ⥤ₑ E is fully faithful.

Defined in

Mathlib.CategoryTheory.Abelian.SerreClass.Localization

Cited by

0 results in Mathlib

Foundations

Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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