Definition disp_left_adjoint_data_ptdfunctor_in_moncat : disp_left_adjoint_data (D := bidisp_monbicat_disp_prebicat) adj_equivalence_ptdfunctor_in_cat (ptdob_to_ptdptdob_fmonoidal Mon_V). Proof. exists (ptdptdob_to_ptdob_fmonoidal Mon_V). split. + use tpair. * intro ; intros. abstract ( use total2_paths_f ; [ simpl ; rewrite (bifunctor_leftid Mon_V) ; rewrite (bifunctor_rightid Mon_V) ; rewrite ! id_right ; apply idpath | apply homset_property ] ). * abstract (use total2_paths_f ; [apply idpath | apply homset_property ]). + use tpair. * intro ; intros. abstract ( use total2_paths_f ; [ use total2_paths_f ; [ simpl ; rewrite (bifunctor_leftid Mon_V) ; rewrite (bifunctor_rightid Mon_V) ; rewrite ! id_right ; apply idpath | apply homset_property ] | apply homset_property ] ). * abstract ( use total2_paths_f ; [ use total2_paths_f ; [ simpl ; rewrite ! id_right ; apply idpath | apply homset_property ] | apply homset_property ] ). 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.coslicecat. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Require Import UniMath.Bicategories.MonoidalCategories.PointedFunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.MonoidalCategories.BicatOfWhiskeredMonCats. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions.