Definition relmonadmor_iso_from_is_z_iso {C : precategory_data} (D : category) (J : functor C D)(R R': RelMonad J) (α : precategory_RelMonad D J ⟦R, R'⟧) : is_z_isomorphism(C := [C, D]) (nat_trans_RelMonadMor α) → z_iso(C := category_RelMonad D J) R R'. Proof. intro T. exists α. exact (is_relmonadmor_z_iso_from_is_z_iso D J α T). 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.