Proposition enriched_relation_conj_fun_right {X Y Z : hSet} (R : enriched_relation V X Y) (f : Z → Y) : R ·e f^o = fun_comp_enriched_relation R (idfun _) f. Proof. use eq_enriched_relation. - intros x z. use CoproductArrow. intro y. use arrow_from_tensor_coproduct_benabou_cosmos. intro p ; cbn. induction p. apply mon_runitor. - intros x z. exact (mon_rinvunitor _ · (identity _ #⊗ CoproductIn _ _ _ (idpath _)) · CoproductIn _ _ _ (f z)). 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.