Theorems · Definition · category theory

CategoryTheory.Functor.ShiftSequence.induced.shiftIso

{C : Type u_1} →
  {D : Type u_2} →
    {A : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} A] →
            (L : CategoryTheory.Functor C D) →
              (G : CategoryTheory.Functor C A) →
                (M : Type u_4) →
                  [inst_3 : AddMonoid M] →
                    [inst_4 : CategoryTheory.HasShift C M] →
                      [inst_5 : G.ShiftSequence M] →
                        (F' : M → CategoryTheory.Functor D A) →
                          ((m : M) → L.comp (F' m) ≅ G.shift m) →
                            [((CategoryTheory.Functor.whiskeringLeft C D A).obj L).Full] →
                              [((CategoryTheory.Functor.whiskeringLeft C D A).obj L).Faithful] →
                                [inst_8 : CategoryTheory.HasShift D M] →
                                  [L.CommShift M] →
                                    (n a a' : M) → n + a = a' → ((CategoryTheory.shiftFunctor D n).comp (F' a) ≅ F' a')

The shiftIso field of the induced shift sequence.

Defined in

Mathlib.CategoryTheory.Shift.InducedShiftSequence

Cited by

2 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequenceCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.HasShiftCategoryTheory.Functor.CommShift