Definition adjequiv_to_weq (X Y : one_types) : (pr1 X ≃ pr1 Y) ≃ adjoint_equivalence X Y. Proof. use weqfibtototal. intro f. apply weqimplimpl. - intro Hf. exact (weq_is_adjoint_equivalence f Hf). - exact (adjoint_equivalence_is_weq f). - apply isapropisweq. - apply isaprop_left_adjoint_equivalence. exact one_types_is_univalent_2_1. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique.