Theorems · Definition · category theory

CategoryTheory.SingleFunctors.shiftIso

{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] →
        {A : Type u_5} →
          [inst_2 : AddMonoid A] →
            [inst_3 : CategoryTheory.HasShift D A] →
              (self : CategoryTheory.SingleFunctors C D A) →
                (n a a' : A) → n + a = a' → ((self.functor a').comp (CategoryTheory.shiftFunctor D n) ≅ self.functor a)

the isomorphism functor a' ⋙ shiftFunctor D n ≅ functor a when n + a = a'

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

26 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShift