Theorems · Definition · category theory

CategoryTheory.HasShift.Induced.zero

{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] →
        (F : CategoryTheory.Functor C D) →
          {A : Type u_3} →
            [inst_2 : AddMonoid A] →
              [inst_3 : CategoryTheory.HasShift C A] →
                (s : A → CategoryTheory.Functor D D) →
                  ((a : A) → F.comp (s a) ≅ (CategoryTheory.shiftFunctor C a).comp F) →
                    [((CategoryTheory.Functor.whiskeringLeft C D D).obj F).Full] →
                      [((CategoryTheory.Functor.whiskeringLeft C D D).obj F).Faithful] →
                        s 0 ≅ CategoryTheory.Functor.id D

The zero field of the ShiftMkCore structure for the induced shift.

Defined in

Mathlib.CategoryTheory.Shift.Induced

Cited by

3 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful