Lemma Initial_WOSET : Initial WOSET. Proof. use make_Initial. - exact empty_woset. - apply make_isInitial; intro a. use tpair. + simpl; intro e; induction e. + abstract (intro f; apply funextfun; intro e; induction e). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.OrderedSets. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Limits. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.exponentials.