Theorems · Theorem · category theory

CategoryTheory.Functor.LaxMonoidal.tensorUnit_whiskerLeft_comp_leftUnitor_hom_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) [inst_4 : F.LaxMonoidal] {X : C} {Y : D} (f : Y ⟶ F.obj X) {Z : D} (h : F.obj X ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (CategoryTheory.MonoidalCategoryStruct.tensorUnit D) f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.leftUnitor (F.obj X)).hom h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.Functor.LaxMonoidal.ε F) f)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.LaxMonoidal.μ F (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X)
        (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 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.LaxMonoidal