Theorems · Theorem · category theory

CategoryTheory.Functor.CoreMonoidal.left_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.CoreMonoidal) (X : C) {Z : D} (h : F.obj X ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.leftUnitor (F.obj X)).hom h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight self.εIso.hom (F.obj X))
      (CategoryTheory.CategoryStruct.comp (self.μIso (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X).hom
        (CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom) h))

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

0 results in Mathlib

Foundations

Depth 6 from the axioms · uses Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory