Definition rKleisli_functor_left_right_compose {C: precategory} {D : precategory} (hs : has_homsets D) {J : functor C D} (R: RelMonad J) : (Left_rKleisli_functor R) ∙ (Right_rKleisli_functor R) = R_functor R. Proof. use functor_eq. - exact hs. - use functor_data_eq_from_nat_trans. + intro a; apply idpath. + intros a b f; simpl. rewrite id_right. rewrite id_left. 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.