Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_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) {Z : F.obj a ⟶ G.obj a}
  (h : CategoryTheory.CategoryStruct.comp (α.app a) (G.map (CategoryTheory.CategoryStruct.id a)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (α.naturality (CategoryTheory.CategoryStruct.id a)).hom h =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (F.mapId a).hom (α.app a))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.leftUnitor (α.app a)).hom
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor (α.app a)).inv
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (α.app a) (G.mapId a).inv) 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