Theorems · Definition · category theory

CategoryTheory.Functor.CommShift.isoZero

{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] →
                  (CategoryTheory.shiftFunctor C 0).comp F ≅ F.comp (CategoryTheory.shiftFunctor D 0)

For any functor F : C ⥤ D, this is the obvious isomorphism shiftFunctor C (0 : A) ⋙ F ≅ F ⋙ shiftFunctor D (0 : A) deduced from the isomorphisms shiftFunctorZero on both categories C and D.

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

8 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShift