Definition subtype_to_nat_trans : subtype_to_functor ⟹ yoneda_objects (po_category P) x. Proof. use make_nat_trans. -- intros y Hyx. exact (pr1 Hyx). -- abstract ( do 3 intro; apply funextfun; intro; apply propproperty ). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.GrothendieckToposes.Sieves. Require Import UniMath.CategoryTheory.Categories.PreorderCategory.Core. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Subobjects. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.OrderTheory.Preorders. Require Import UniMath.CategoryTheory.yoneda. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.slicecat.