Theorems · Theorem · category theory

CategoryTheory.Oplax.LaxTrans.vComp_naturality_id

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {F G H : CategoryTheory.OplaxFunctor B C} (η : CategoryTheory.Oplax.LaxTrans F G)
  (θ : CategoryTheory.Oplax.LaxTrans G H) (a : B),
  CategoryTheory.CategoryStruct.comp (η.vCompNaturality θ (CategoryTheory.CategoryStruct.id a))
      (CategoryTheory.Bicategory.whiskerRight (F.mapId a) (η.vCompApp θ a)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (η.vCompApp θ a) (H.mapId a))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.rightUnitor (η.vCompApp θ a)).hom
        (CategoryTheory.Bicategory.leftUnitor (η.vCompApp θ a)).inv)

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax

Cited by

0 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory