Definition sigma_bicat_data : disp_prebicat_data C. Proof. exists sigma_prebicat_1_id_comp_cells. repeat split; cbn; first [intros * | intros]. - exists (disp_id2 _). exact (disp_id2 _). - exists (disp_lunitor (pr1 f')). exact (disp_lunitor (pr2 f')). - exists (disp_runitor (pr1 f')). exact (disp_runitor (pr2 f')). - exists (disp_linvunitor (pr1 f')). exact (disp_linvunitor (pr2 f')). - exists (disp_rinvunitor (pr1 f')). exact (disp_rinvunitor (pr2 f')). - exists (disp_rassociator (pr1 ff) (pr1 gg) (pr1 hh)). exact (disp_rassociator (pr2 ff) (pr2 gg) (pr2 hh)). - exists (disp_lassociator (pr1 ff) (pr1 gg) (pr1 hh)). exact (disp_lassociator (pr2 ff) (pr2 gg) (pr2 hh)). - intros xx yy. exists (disp_vcomp2 (pr1 xx) (pr1 yy)). exact (disp_vcomp2 (pr2 xx) (pr2 yy)). - intros xx. exists (disp_lwhisker (pr1 ff) (pr1 xx)). exact (disp_lwhisker (pr2 ff) (pr2 xx)). - intros xx. exists (disp_rwhisker (pr1 gg) (pr1 xx)). exact (disp_rwhisker (pr2 gg) (pr2 xx)). 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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.