Theorems · Theorem · category theory

CategoryTheory.Functor.LaxMonoidal.left_unitality

∀ {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.LaxMonoidal] (X : C),
  (CategoryTheory.MonoidalCategoryStruct.leftUnitor (F.obj X)).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.Functor.LaxMonoidal.ε F) (F.obj X))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.LaxMonoidal.μ F (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X)
        (F.map (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom))

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

6 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.Functor.LaxMonoidal