Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app

∀ {B : Type u_1} [inst : CategoryTheory.Bicategory B] {F G : CategoryTheory.Pseudofunctor B CategoryTheory.Cat}
  (α : F ⟶ G) {a b : B} {f g : a ⟶ b} (η : f ≅ g) (X : ↑(F.obj a)),
  (α.naturality g).hom.toNatTrans.app X =
    CategoryTheory.CategoryStruct.comp ((α.app b).toFunctor.map ((F.map₂ η.inv).toNatTrans.app X))
      (CategoryTheory.CategoryStruct.comp ((α.naturality f).hom.toNatTrans.app X)
        ((G.map₂ η.hom).toNatTrans.app ((α.app a).toFunctor.obj X)))

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Bicategory