Lemma has_homsets_cat_of_elems {C : category} (X : C^op ⟶ HSET) : has_homsets (precat_of_elems X). Proof. intros a b. apply isaset_total2. - apply C. - intro f. apply isasetaprop, setproperty. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf.