Theorems · Theorem · category theory

CategoryTheory.Lax.LaxTrans.vComp_naturality_comp

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {F G H : CategoryTheory.LaxFunctor B C} (η : CategoryTheory.Lax.LaxTrans F G) (θ : CategoryTheory.Lax.LaxTrans G H)
  {a b c : B} (f : a ⟶ b) (g : b ⟶ c),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (η.vCompApp θ a) (H.mapComp f g))
      (η.vCompNaturality θ (CategoryTheory.CategoryStruct.comp f g)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator (η.vCompApp θ a) (H.map f) (H.map g)).inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (η.vCompNaturality θ f) (H.map g))
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.Bicategory.associator (F.map f) (η.vCompApp θ b) (H.map g)).hom
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (η.vCompNaturality θ g))
            (CategoryTheory.CategoryStruct.comp
              (CategoryTheory.Bicategory.associator (F.map f) (F.map g) (η.vCompApp θ c)).inv
              (CategoryTheory.Bicategory.whiskerRight (F.mapComp f g) (η.vCompApp θ c))))))

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax

Cited by

0 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory