Theorems · Definition · category theory

CategoryTheory.Oplax.StrongTrans.Modification.mk.noConfusion

{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} →
            {P : Sort u} →
              {app : (a : B) → η.app a ⟶ θ.app a} →
                {naturality :
                    autoParam
                      (∀ {a b : B} (f : a ⟶ b),
                        CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (app b))
                            (θ.naturality f).hom =
                          CategoryTheory.CategoryStruct.comp (η.naturality f).hom
                            (CategoryTheory.Bicategory.whiskerRight (app a) (G.map f)))
                      CategoryTheory.Oplax.StrongTrans.Modification.naturality._autoParam} →
                  {app' : (a : B) → η.app a ⟶ θ.app a} →
                    {naturality' :
                        autoParam
                          (∀ {a b : B} (f : a ⟶ b),
                            CategoryTheory.CategoryStruct.comp
                                (CategoryTheory.Bicategory.whiskerLeft (F.map f) (app' b)) (θ.naturality f).hom =
                              CategoryTheory.CategoryStruct.comp (η.naturality f).hom
                                (CategoryTheory.Bicategory.whiskerRight (app' a) (G.map f)))
                          CategoryTheory.Oplax.StrongTrans.Modification.naturality._autoParam} →
                      { app := app, naturality := naturality } = { app := app', naturality := naturality' } →
                        (app ≍ app' → P) → P

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Oplax

Cited by

1 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound