Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.StrongTrans.naturality

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {F G : CategoryTheory.Pseudofunctor B C} →
          (self : F.StrongTrans G) →
            {a b : B} →
              (f : a ⟶ b) →
                CategoryTheory.CategoryStruct.comp (F.map f) (self.app b) ≅
                  CategoryTheory.CategoryStruct.comp (self.app a) (G.map f)

The 2-isomorphisms underlying the strong naturality constraint.

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo

Cited by

81 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory