Proposition is_colim_enriched_is_wedge (a : enriched_colim_cocone) (w : C) : is_wedge (weighted_hom_co w) (is_colim_enriched_wedge_data a w). Proof. intros i j g ; cbn. rewrite !functor_id. rewrite (functor_id W). rewrite precomp_arr_id. use internal_funext. intros z h. rewrite !tensor_comp_r_id_r. rewrite !assoc'. unfold internal_pre_post_comp. rewrite !internal_beta. rewrite !tensor_id_id. rewrite id_left, id_right. rewrite !assoc. rewrite <- tensor_comp_mor. rewrite id_right. rewrite tensor_split. rewrite !assoc'. rewrite internal_beta. refine (!_). rewrite tensor_split. rewrite !assoc'. rewrite !(maponpaths (λ z, _ · z) (assoc _ _ _)). rewrite internal_beta. rewrite tensor_comp_id_l. rewrite !assoc'. apply maponpaths. rewrite enriched_comp_precomp_arr. rewrite !assoc. rewrite <- !tensor_comp_id_l. apply maponpaths_2. apply maponpaths. apply enriched_colim_cocone_commute. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.OppositeCategory.Core. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Ends. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedConicalColimits. Require Import UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCopowers. Import MonoidalNotations.