Theorems · Definition · category theory

CategoryTheory.Functor.CommShift.ofComp

{C : Type u_1} →
  {D : Type u_2} →
    {E : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
            {F : CategoryTheory.Functor C D} →
              {G : CategoryTheory.Functor D E} →
                {H : CategoryTheory.Functor C E} →
                  (F.comp G ≅ H) →
                    [G.Full] →
                      [G.Faithful] →
                        (A : Type u_5) →
                          [inst_5 : AddMonoid A] →
                            [inst_6 : CategoryTheory.HasShift C A] →
                              [inst_7 : CategoryTheory.HasShift D A] →
                                [inst_8 : CategoryTheory.HasShift E A] →
                                  [G.CommShift A] → [H.CommShift A] → F.CommShift A

Given an isomorphism e : F ⋙ G ≅ H where G is fully faithful, the functor F commutes with shifts by A if G and H do.

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShift