proposition: Lemma psfunctor_preserve_adj_equiv {C D : bicat} (F : psfunctor C D) (x y : C) : adjoint_equivalence x y -> adjoint_equivalence (pr111 F x) (pr111 F y).
proof: Proof. intro a. exists (pr211 F _ _ (pr1 a)). use psfunctor_preserves_adjequiv'. exact (pr2 a). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.CategoryTheory.DisplayedCats.Core UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.PseudoFunctors.Display.Base UniMath.Bicategories.PseudoFunctors.Display.Map1Cells UniMath.Bicategories.PseudoFunctors.Display.Map2Cells UniMath.Bicategories.PseudoFunctors.Display.Identitor UniMath.Bicategories.PseudoFunctors.Display.Compositor UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat