Theorems · Theorem · category theory

CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality

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

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Oplax

Cited by

2 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory