Definition monbicat_disp_locally_groupoid : disp_locally_groupoid bidisp_monbicat_disp_bicat. Proof. red. intros C D F G αiso M N Fm Gm ismnt. use tpair. - transparent assert (isnziα : (is_nat_z_iso (pr11 αiso))). { apply (nat_trafo_pointwise_z_iso_if_z_iso (pr2 D)). exact (pr2 αiso). } exact (is_mon_nat_trans_pointwise_inverse (Fm : fmonoidal _ _ _) (Gm : fmonoidal _ _ _) (pr1 αiso) isnziα ismnt). - split; apply isaprop_bidisp_monbicat_disp_2cell_struct. 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.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Import BifunctorNotations.