Theorems · Theorem · category theory

CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_id

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {F G : CategoryTheory.OplaxFunctor B C} (η : CategoryTheory.Oplax.StrongTrans F G) {a : B} {a' : C}
  (f : G.obj a ⟶ a'),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Bicategory.whiskerRight (η.naturality (CategoryTheory.CategoryStruct.id a)).hom f)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Bicategory.associator (η.app a) (G.map (CategoryTheory.CategoryStruct.id a)) f).hom
        (CategoryTheory.Bicategory.whiskerLeft (η.app a) (CategoryTheory.Bicategory.whiskerRight (G.mapId a) f))) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Bicategory.whiskerRight (CategoryTheory.Bicategory.whiskerRight (F.mapId a) (η.app a)) f)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Bicategory.whiskerRight (CategoryTheory.Bicategory.leftUnitor (η.app a)).hom f)
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.Bicategory.whiskerRight (CategoryTheory.Bicategory.rightUnitor (η.app a)).inv f)
          (CategoryTheory.Bicategory.associator (η.app a) (CategoryTheory.CategoryStruct.id (G.obj a)) f).hom))

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax

Cited by

3 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory