Theorems · Theorem · category theory

CategoryTheory.Oplax.StrongTrans.categoryStruct_comp_naturality

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {X Y Z : CategoryTheory.OplaxFunctor B C} (η : CategoryTheory.Oplax.StrongTrans X Y)
  (θ : CategoryTheory.Oplax.StrongTrans Y Z) {a b : B} (f : a ⟶ b),
  (CategoryTheory.CategoryStruct.comp η θ).naturality f =
    (CategoryTheory.Bicategory.associator (X.map f) (η.app b) (θ.app b)).symm ≪≫
      CategoryTheory.Bicategory.whiskerRightIso (η.naturality f) (θ.app b) ≪≫
        CategoryTheory.Bicategory.associator (η.app a) (Y.map f) (θ.app b) ≪≫
          CategoryTheory.Bicategory.whiskerLeftIso (η.app a) (θ.naturality f) ≪≫
            (CategoryTheory.Bicategory.associator (η.app a) (θ.app a) (Z.map f)).symm

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory