Theorems · Theorem · category theory

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

The naturality condition.

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Oplax

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory