Lemma has_homsets_RelMonad {C : precategory_data} {D : precategory} (hs: has_homsets D) (J : functor_data C D) : has_homsets (precategory_RelMonad hs J). Proof. intros R R'. simpl. unfold RelMonadMor. apply isaset_total2 . - apply impred_isaset. intro. apply hs. - intro α. apply isasetaprop. apply isaprop_RelMonadMor_axioms. apply hs. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core.