Theorems · Definition · category theory

CategoryTheory.Functor.shiftIso

{C : Type u_1} →
  {A : Type u_3} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_3, u_3} A] →
        (F : CategoryTheory.Functor C A) →
          {M : Type u_4} →
            [inst_2 : AddMonoid M] →
              [inst_3 : CategoryTheory.HasShift C M] →
                [inst_4 : F.ShiftSequence M] →
                  (n a a' : M) → n + a = a' → ((CategoryTheory.shiftFunctor C n).comp (F.shift a) ≅ F.shift a')

Compatibility isomorphism shiftFunctor C n ⋙ F.shift a ≅ F.shift a' when n + a = a'.

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

36 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence