Theorems · Theorem · category theory

CategoryTheory.Functor.OplaxMonoidal.right_unitality_assoc

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C} {D : Type u₂}
  {inst_2 : CategoryTheory.Category.{v₂, u₂} D} {inst_3 : CategoryTheory.MonoidalCategory D}
  (F : CategoryTheory.Functor C D) [self : F.OplaxMonoidal] (X : C) {Z : D}
  (h :
    CategoryTheory.MonoidalCategoryStruct.tensorObj (F.obj X) (CategoryTheory.MonoidalCategoryStruct.tensorUnit D) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.rightUnitor (F.obj X)).inv h =
    CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).inv)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.OplaxMonoidal.δ F X (CategoryTheory.MonoidalCategoryStruct.tensorUnit C))
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (F.obj X) (CategoryTheory.Functor.OplaxMonoidal.η F)) h))

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

0 results in Mathlib

Foundations

Depth 6 from the axioms · uses Quot.sound

Assumes

CategoryTheory.Functor.OplaxMonoidal