fact: Definition disp_adj_weq_preserves_initial : disp_adjunction a CC₁ CC₂ ≃ preserves_initial (pr112 a).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Preservation UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Examples.StructuredCategories UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Morphisms.Examples.MorphismsInBicatOfUnivCats UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell