Theorems · Definition · category theory

CategoryTheory.Functor.CommShift.ofIso

{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 G : CategoryTheory.Functor C D} →
          (F ≅ G) →
            (A : Type u_4) →
              [inst_2 : AddMonoid A] →
                [inst_3 : CategoryTheory.HasShift C A] →
                  [inst_4 : CategoryTheory.HasShift D A] → [F.CommShift A] → G.CommShift A

If e : F ≅ G is an isomorphism of functors and if F commutes with the shift, then G also commutes with the shift.

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShift