proposition: Lemma forgetRelMonad_faithful {C : precategory} (D : category) (J : functor C D) : faithful (forgetfunctor_RelMonad D J).
proof: Proof. intros R R'. simpl. apply isinclbetweensets. - apply isaset_total2. + apply impred_isaset. intros. apply D. + intros. apply isasetaprop. apply isaprop_RelMonadMor_axioms. apply D. - apply isaset_nat_trans. apply D. - intros α α' p. apply RelMonadMor_equiv. + apply D. + apply funextsec. intro c. change (nat_trans_RelMonadMor α c = nat_trans_RelMonadMor α' c). rewrite p. apply idpath. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core