Theorems · Definition · category theory

CategoryTheory.Functor.commShiftOfLocalization

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {E : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} E] →
            (L : CategoryTheory.Functor C D) →
              (W : CategoryTheory.MorphismProperty C) →
                [L.IsLocalization W] →
                  (A : Type w) →
                    [inst_4 : AddMonoid A] →
                      [inst_5 : CategoryTheory.HasShift C A] →
                        (F : CategoryTheory.Functor C E) →
                          (F' : CategoryTheory.Functor D E) →
                            [CategoryTheory.Localization.Lifting L W F F'] →
                              [inst_7 : CategoryTheory.HasShift D A] →
                                [inst_8 : CategoryTheory.HasShift E A] →
                                  [L.CommShift A] → [F.CommShift A] → F'.CommShift A

In the context of localization of categories, if a functor is induced by a functor which commutes with the shift, then this functor commutes with the shift.

Defined in

Mathlib.CategoryTheory.Shift.Localization

Cited by

2 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationAddMonoidCategoryTheory.HasShiftCategoryTheory.Localization.LiftingCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShift