Theorems · Definition · category theory

CategoryTheory.Adjunction.LeftAdjointCommShift.iso

{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} →
          {G : CategoryTheory.Functor D C} →
            (F ⊣ G) →
              {A : Type u_3} →
                [inst_2 : AddGroup A] →
                  [inst_3 : CategoryTheory.HasShift C A] →
                    [inst_4 : CategoryTheory.HasShift D A] →
                      (a : A) →
                        [G.CommShift A] →
                          (CategoryTheory.shiftFunctor C a).comp F ≅ F.comp (CategoryTheory.shiftFunctor D a)

Given an adjunction F ⊣ G and a CommShift structure on G, these are the candidate CommShift.iso a isomorphisms for a compatible CommShift structure on F.

Defined in

Mathlib.CategoryTheory.Shift.Adjunction

Cited by

6 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddGroupCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShift