Theorems · Definition · category theory

CategoryTheory.shiftShiftNeg

{C : Type u} →
  {A : Type u_1} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : AddGroup A] →
        [inst_2 : CategoryTheory.HasShift C A] →
          (X : C) → (i : A) → (CategoryTheory.shiftFunctor C (-i)).obj ((CategoryTheory.shiftFunctor C i).obj X) ≅ X

Shifting by i and then shifting by -i is the identity.

Defined in

Mathlib.CategoryTheory.Shift.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryAddGroupCategoryTheory.HasShift