Definition subtype_to_sieve (f : downward_closed_subtype (subpreorder P (down_type P x))) : sieve (C := po_category P) x := (subtype_to_functor f ,, tt) ,, make_Monic ([_, _]) (subtype_to_nat_trans f) (subtype_to_isMonic f).
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.