Theorems · Definition · category theory

CategoryTheory.Functor.Braided.casesOn

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        {D : Type u₂} →
          [inst_3 : CategoryTheory.Category.{v₂, u₂} D] →
            [inst_4 : CategoryTheory.MonoidalCategory D] →
              [inst_5 : CategoryTheory.BraidedCategory D] →
                {F : CategoryTheory.Functor C D} →
                  {motive : F.Braided → Sort u} →
                    (t : F.Braided) →
                      ([toMonoidal : F.Monoidal] →
                          (braided :
                              ∀ (X Y : C),
                                CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ F X Y)
                                    (F.map (β_ X Y).hom) =
                                  CategoryTheory.CategoryStruct.comp (β_ (F.obj X) (F.obj Y)).hom
                                    (CategoryTheory.Functor.LaxMonoidal.μ F Y X)) →
                            motive { toMonoidal := toMonoidal, braided := braided }) →
                        motive t

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

1 results in Mathlib

Foundations

Depth 11 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory