Theorems · Definition · category theory

CategoryTheory.Functor.shiftMap

{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] →
                  {X Y : C} →
                    {n : M} →
                      (X ⟶ (CategoryTheory.shiftFunctor C n).obj Y) →
                        (a a' : M) → n + a = a' → ((F.shift a).obj X ⟶ (F.shift a').obj Y)

The morphism (F.shift a).obj X ⟶ (F.shift a').obj Y induced by a morphism f : X ⟶ Y⟦n⟧ when n + a = a'.

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

24 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence