Theorems · Definition · category theory

CategoryTheory.Functor.CommShift.isoAdd

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {F : CategoryTheory.Functor C D} →
          {A : Type u_4} →
            [inst_2 : AddMonoid A] →
              [inst_3 : CategoryTheory.HasShift C A] →
                [inst_4 : CategoryTheory.HasShift D A] →
                  {a b : A} →
                    ((CategoryTheory.shiftFunctor C a).comp F ≅ F.comp (CategoryTheory.shiftFunctor D a)) →
                      ((CategoryTheory.shiftFunctor C b).comp F ≅ F.comp (CategoryTheory.shiftFunctor D b)) →
                        ((CategoryTheory.shiftFunctor C (a + b)).comp F ≅
                          F.comp (CategoryTheory.shiftFunctor D (a + b)))

If a functor F : C ⥤ D is equipped with "commutation isomorphisms" with the shifts by a and b, then there is a commutation isomorphism with the shift by a + b.

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

5 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShift