Theorems · Theorem · category theory

CategoryTheory.Lax.StrongTrans.naturality_naturality_assoc

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {F G : CategoryTheory.LaxFunctor B C} (self : CategoryTheory.Lax.StrongTrans F G) {a b : B} {f g : a ⟶ b} (η : f ⟶ g)
  {Z : F.obj a ⟶ G.obj b} (h : CategoryTheory.CategoryStruct.comp (F.map g) (self.app b) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (self.naturality f).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.map₂ η) (self.app b)) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (self.app a) (G.map₂ η))
      (CategoryTheory.CategoryStruct.comp (self.naturality g).hom h)

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax

Cited by

0 results in Mathlib

Foundations

Depth 7 from the axioms · uses Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory