Theorems · Definition · category theory

CategoryTheory.Functor.ShiftSequence.leftComp

{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] →
            {F : CategoryTheory.Functor C A} →
              {π : CategoryTheory.Functor C D} →
                {H : CategoryTheory.Functor D A} →
                  (π.comp H ≅ F) →
                    (M : Type u_4) →
                      [inst_3 : AddMonoid M] →
                        [inst_4 : CategoryTheory.HasShift C M] →
                          [inst_5 : CategoryTheory.HasShift D M] →
                            [π.CommShift M] → [H.ShiftSequence M] → F.ShiftSequence M

Given an isomorphism π ⋙ H ≅ F, where π is a functor which commutes with the shift by M and H is equipped with a shift sequence, then this is the shift sequence for F induced by composition.

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

3 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.ShiftSequence