Theorems · Definition · category theory

CategoryTheory.shiftComm

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

When shifts are indexed by an additive commutative monoid, then shifts commute.

Defined in

Mathlib.CategoryTheory.Shift.Basic

Cited by

9 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddCommMonoidCategoryTheory.HasShift