Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app

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