Theorems · Definition · category theory

CategoryTheory.Lax.LaxTrans.vCompNaturality

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {C : Type u₂} →
      [inst_1 : CategoryTheory.Bicategory C] →
        {F G H : CategoryTheory.LaxFunctor B C} →
          (η : CategoryTheory.Lax.LaxTrans F G) →
            (θ : CategoryTheory.Lax.LaxTrans G H) →
              {a b : B} →
                (f : a ⟶ b) →
                  CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp (η.app a) (θ.app a))
                      (H.map f) ⟶
                    CategoryTheory.CategoryStruct.comp (F.map f)
                      (CategoryTheory.CategoryStruct.comp (η.app b) (θ.app b))

Auxiliary definition for vComp.

Defined in

Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax

Cited by

3 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory