Theorems · Definition · category theory

CategoryTheory.shiftFunctorCompIsoId

(C : Type u) →
  {A : Type u_1} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : AddMonoid A] →
        [inst_2 : CategoryTheory.HasShift C A] →
          (i j : A) →
            i + j = 0 →
              ((CategoryTheory.shiftFunctor C i).comp (CategoryTheory.shiftFunctor C j) ≅ CategoryTheory.Functor.id C)

When i + j = 0, shifting by i and by j gives the identity functor

Defined in

Mathlib.CategoryTheory.Shift.Basic

Cited by

69 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShift