Definition weq_op2_left_adjequiv {B : bicat} {x y : op2_bicat B} (f : x --> y) : @left_adjoint_equivalence B x y f ≃ left_adjoint_equivalence f. Proof. use make_weq. - exact (to_op2_left_adjequiv f). - use isweq_iso. + exact (from_op2_left_adjequiv f). + abstract (intros Hf ; refine (maponpaths (λ z, _ ,, z) _) ; apply isapropdirprod ; [ apply isapropdirprod ; apply cellset_property | apply isapropdirprod ; apply isaprop_is_invertible_2cell ]). + abstract (intros Hf ; refine (maponpaths (λ z, _ ,, z) _) ; apply isapropdirprod ; [ apply isapropdirprod ; apply cellset_property | apply isapropdirprod ; apply isaprop_is_invertible_2cell ]). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions.