Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_inv

∀ {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),
  (α.naturality g).inv =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (α.app a) (G.map₂ η.inv))
      (CategoryTheory.CategoryStruct.comp (α.naturality f).inv
        (CategoryTheory.Bicategory.whiskerRight (F.map₂ η.hom) (α.app b)))

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory