Theorems · Theorem · category theory

CategoryTheory.Oplax.OplaxTrans.whiskerLeft_naturality_id_assoc

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

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax

Cited by

0 results in Mathlib

Foundations

Depth 8 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory