Proposition comp_conjoint_companion_enriched_relation {X Y : hSet} (f : X → Y) : enriched_relation_le (f^o ·e f^*) (id_enriched_relation _). Proof. intros y y'. use CoproductArrow ; cbn. intro x. use arrow_from_tensor_coproduct_benabou_cosmos. intro p. refine (sym_mon_braiding _ _ _ · _). use arrow_from_tensor_coproduct_benabou_cosmos. intro q. cbn. refine (_ · CoproductIn _ _ _ _). - apply mon_lunitor. - exact (!q @ 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.