Definition unit_actegory : actegory Mon_V (pr1 unit_category). Proof. use tpair. - use tpair. + use make_bifunctor_data. * exact (fun _ _ => tt). * intros. apply idpath. * intros. apply idpath. + cbn. repeat split; intro x; induction x; apply isapropunit. - cbn. split. + repeat split; intro x; induction x; apply isapropunit. + cbn. abstract (split; [| split; [| split]]; [red; split; red; intros; [apply isasetunit | split; apply isasetunit] | red; do 3 (split; [red; intros; apply isasetunit |]); split; apply isasetunit | red; intros; apply isasetunit | 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.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. 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.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.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.Bicategories.MonoidalCategories.BicatOfActegories. Import BifunctorNotations.