Definition forgetfunctor_RelMonad {C : precategory} (D : category) (J : functor C D) : functor (category_RelMonad D J) (functor_category C D). Proof. use make_functor. - simpl. use make_functor_data. + simpl. exact (λ R : RelMonad J, R_functor R). + simpl. intros R R' α. exact (nat_trans_RelMonadMor α). - split. + red. intros. simpl. apply nat_trans_eq. * apply D. * intros; apply idpath. + unfold functor_compax. simpl. intros R R' R'' α α'. apply nat_trans_eq. * apply D. * intro c. apply idpath. 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.