Definition unit_monoidal : monoidal (pr1 unit_category). Proof. use tpair. - use tpair. + use make_bifunctor_data. * exact (fun _ _ => tt). * intros. apply idpath. * intros. apply idpath. + exists tt. repeat split; intro x; induction x; apply isapropunit. - split. + abstract (repeat split). + abstract ( do 2 (split; [split; red; intros; [apply isasetunit | split; apply isasetunit] |]); split; [ do 3 (split; [red; intros; apply isasetunit |]); split; apply isasetunit | split; red; intros; apply isasetunit]). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.Limits.Final. Require Import UniMath.Bicategories.Limits.Examples.BicatOfCatsLimits. Require Import UniMath.Bicategories.Limits.Examples.TotalBicategoryLimits. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.Bicategories.MonoidalCategories.BicatOfWhiskeredMonCats.