proposition: Proposition copower_from_colim_wedge_inv_1 : is_copower_enriched_map E v x copower_from_colim_cocone w · mor_to_end (weighted_hom_co E D W w) (pr2 a w) copower_from_colim_wedge = identity _.
proof: Proof. use (mor_to_end_eq _ (pr2 a w)). intro i. rewrite !assoc'. etrans. { apply maponpaths. exact (mor_to_end_comm _ (pr2 a w) copower_from_colim_wedge i). } refine (id_right _ @ _ @ !(id_left _)). use internal_funext. intros z h. rewrite tensor_split. rewrite !assoc'. unfold is_copower_enriched_map. rewrite internal_beta. refine (!_). rewrite tensor_split. rewrite !assoc'. apply maponpaths. etrans. { apply internal_beta. } induction i. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Ends UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedConicalColimits UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCopowers