Theorems · Theorem · category theory

CategoryTheory.Oplax.LaxTrans.Modification.whiskerLeft_naturality_assoc

∀ {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.LaxTrans.Modification η θ) {a b : B}
  {a' : C} (f : a' ⟶ F.obj a) (g : a ⟶ b) {Z : a' ⟶ G.obj b}
  (h : CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.comp (F.map g) (θ.app b)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Bicategory.whiskerLeft f (CategoryTheory.Bicategory.whiskerRight (Γ.app a) (G.map g)))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft f (θ.naturality g)) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft f (η.naturality g))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Bicategory.whiskerLeft f (CategoryTheory.Bicategory.whiskerLeft (F.map g) (Γ.app b))) h)

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Oplax

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory