Theorems · Theorem · category theory

CategoryTheory.Oplax.OplaxTrans.whiskerRight_naturality_naturality_assoc

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {F G : CategoryTheory.OplaxFunctor B C} (η : CategoryTheory.Oplax.OplaxTrans F G) {a b : B} {a' : C} {f g : a ⟶ b}
  (β : f ⟶ g) (h : G.obj b ⟶ a') {Z : F.obj a ⟶ a'}
  (h_1 : CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp (η.app a) (G.map g)) h ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Bicategory.whiskerRight (CategoryTheory.Bicategory.whiskerRight (F.map₂ β) (η.app b)) h)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (η.naturality g) h) h_1) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerRight (η.naturality f) h)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator (η.app a) (G.map f) h).hom
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.Bicategory.whiskerLeft (η.app a) (CategoryTheory.Bicategory.whiskerRight (G.map₂ β) h))
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.associator (η.app a) (G.map g) h).inv h_1)))

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax

Cited by

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Foundations

Depth 8 from the axioms · uses Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory