Lemma discrete_category_hom_prop {disc : discrete_category} {a b : ob disc} : isaprop (a --> b). Proof. apply (@isofhlevelweqf _ (a = b)). - apply invweq, (@univalent_groupoid_arrow_weq_path disc). - apply (isaset_ob (_ ,, discrete_category_is_setcategory _)). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat.