Theorems · Definition · category theory

CategoryTheory.Oplax.StrongTrans.isoMk

{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} →
            (app : (a : B) → η.app a ≅ θ.app a) →
              autoParam
                  (∀ {a b : B} (f : a ⟶ b),
                    CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (app b).hom)
                        (θ.naturality f).hom =
                      CategoryTheory.CategoryStruct.comp (η.naturality f).hom
                        (CategoryTheory.Bicategory.whiskerRight (app a).hom (G.map f)))
                  CategoryTheory.Oplax.StrongTrans.isoMk._auto_1 →
                (η ≅ θ)

Construct a modification isomorphism between strong natural transformations (of oplax functors) by giving object level isomorphisms, and checking naturality only in the forward direction.

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Oplax

Cited by

2 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory