Proposition conjoint_enriched_relation_id (X : hSet) : (idfun X)^o = id_enriched_relation X. Proof. use eq_enriched_relation. - intros x y. use CoproductArrow ; cbn. intro p. exact (CoproductIn _ _ _ (!p)). - intros x y. use CoproductArrow ; cbn. intro p. exact (CoproductIn _ _ _ (!p)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.PosetCat. Require Import UniMath.CategoryTheory.Limits.Coends. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations.