Theorems · Definition · category theory

CategoryTheory.HasShift.localized

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (L : CategoryTheory.Functor C D) →
          (W : CategoryTheory.MorphismProperty C) →
            [L.IsLocalization W] →
              (A : Type w) →
                [inst_3 : AddMonoid A] →
                  [inst_4 : CategoryTheory.HasShift C A] → [W.IsCompatibleWithShift A] → CategoryTheory.HasShift D A

When L : C ⥤ D is a localization functor with respect to a morphism property W that is compatible with the shift by a monoid A on C, this is the induced shift on the category D.

Defined in

Mathlib.CategoryTheory.Shift.Localization

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationAddMonoidCategoryTheory.HasShiftCategoryTheory.MorphismProperty.IsCompatibleWithShift