Theorems · Theorem · category theory

CategoryTheory.Lax.LaxTrans.vComp_naturality_naturality

∀ {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 : B} {f g : a ⟶ b} (β : f ⟶ g),
  CategoryTheory.CategoryStruct.comp (η.vCompNaturality θ f)
      (CategoryTheory.Bicategory.whiskerRight (F.map₂ β) (η.vCompApp θ b)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (η.vCompApp θ a) (H.map₂ β))
      (η.vCompNaturality θ g)

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