Definition RelMonad_axioms (R : RelMonad_data) : UU := (∏ c, r_bind R (r_eta R c) = identity _ ) × (∏ c d (f : D⟦J c, R d⟧), r_eta R _ · r_bind R f = f) × (∏ c d e (f : D ⟦J c, R d⟧) (g : D ⟦J d, R e⟧), r_bind R f · r_bind R g = r_bind R (f · r_bind R g)).
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.