Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_assoc

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

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory