Theorems · Definition · category theory

CategoryTheory.PrelaxFunctor.mk.noConfusion

{B : Type u₁} →
  {inst : CategoryTheory.Bicategory B} →
    {C : Type u₂} →
      {inst_1 : CategoryTheory.Bicategory C} →
        {P : Sort u} →
          {toPrelaxFunctorStruct : CategoryTheory.PrelaxFunctorStruct B C} →
            {map₂_id :
                autoParam
                  (∀ {a b : B} (f : a ⟶ b),
                    toPrelaxFunctorStruct.map₂ (CategoryTheory.CategoryStruct.id f) =
                      CategoryTheory.CategoryStruct.id (toPrelaxFunctorStruct.map f))
                  CategoryTheory.PrelaxFunctor.map₂_id._autoParam} →
              {map₂_comp :
                  autoParam
                    (∀ {a b : B} {f g h : a ⟶ b} (η : f ⟶ g) (θ : g ⟶ h),
                      toPrelaxFunctorStruct.map₂ (CategoryTheory.CategoryStruct.comp η θ) =
                        CategoryTheory.CategoryStruct.comp (toPrelaxFunctorStruct.map₂ η)
                          (toPrelaxFunctorStruct.map₂ θ))
                    CategoryTheory.PrelaxFunctor.map₂_comp._autoParam} →
                {toPrelaxFunctorStruct' : CategoryTheory.PrelaxFunctorStruct B C} →
                  {map₂_id' :
                      autoParam
                        (∀ {a b : B} (f : a ⟶ b),
                          toPrelaxFunctorStruct'.map₂ (CategoryTheory.CategoryStruct.id f) =
                            CategoryTheory.CategoryStruct.id (toPrelaxFunctorStruct'.map f))
                        CategoryTheory.PrelaxFunctor.map₂_id._autoParam} →
                    {map₂_comp' :
                        autoParam
                          (∀ {a b : B} {f g h : a ⟶ b} (η : f ⟶ g) (θ : g ⟶ h),
                            toPrelaxFunctorStruct'.map₂ (CategoryTheory.CategoryStruct.comp η θ) =
                              CategoryTheory.CategoryStruct.comp (toPrelaxFunctorStruct'.map₂ η)
                                (toPrelaxFunctorStruct'.map₂ θ))
                          CategoryTheory.PrelaxFunctor.map₂_comp._autoParam} →
                      { toPrelaxFunctorStruct := toPrelaxFunctorStruct, map₂_id := map₂_id, map₂_comp := map₂_comp } =
                          { toPrelaxFunctorStruct := toPrelaxFunctorStruct', map₂_id := map₂_id',
                            map₂_comp := map₂_comp' } →
                        (toPrelaxFunctorStruct ≍ toPrelaxFunctorStruct' → P) → P

Defined in

Mathlib.CategoryTheory.Bicategory.Functor.Prelax

Cited by

1 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms