Proposition enriched_weighted_to_conical_is_conical_colim_is_wedge : is_wedge (weighted_hom_co E D W w) enriched_weighted_to_conical_is_conical_colim_wedge_data. Proof. intros i j f ; cbn. use internal_funext. intros z h. rewrite !tensor_comp_r_id_r. rewrite !assoc'. unfold internal_pre_post_comp. rewrite !internal_beta. rewrite functor_id. rewrite precomp_arr_id. rewrite id_right. rewrite !tensor_id_id. rewrite !id_left. rewrite tensor_split. rewrite !assoc'. rewrite internal_beta. refine (!_). rewrite tensor_split. rewrite !assoc'. rewrite (maponpaths (λ z, _ · z) (assoc _ _ _)). rewrite internal_beta. rewrite !assoc'. do 2 apply maponpaths. apply ps. 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.