Theorems · Definition · category theory

CategoryTheory.NatTrans.CommShiftCore.recOn

{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] →
        {F₁ F₂ : CategoryTheory.Functor C D} →
          {τ : F₁ ⟶ F₂} →
            {A : Type u_5} →
              [inst_2 : AddMonoid A] →
                [inst_3 : CategoryTheory.HasShift C A] →
                  [inst_4 : CategoryTheory.HasShift D A] →
                    [inst_5 : F₁.CommShift A] →
                      [inst_6 : F₂.CommShift A] →
                        {a : A} →
                          {motive : CategoryTheory.NatTrans.CommShiftCore τ a → Sort u} →
                            (t : CategoryTheory.NatTrans.CommShiftCore τ a) →
                              ((shift_comm :
                                    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.commShiftIso F₁ a).hom
                                        (CategoryTheory.Functor.whiskerRight τ (CategoryTheory.shiftFunctor D a)) =
                                      CategoryTheory.CategoryStruct.comp
                                        ((CategoryTheory.shiftFunctor C a).whiskerLeft τ)
                                        (CategoryTheory.Functor.commShiftIso F₂ a).hom) →
                                  motive ⋯) →
                                motive t

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShift