proposition: Proposition is_conical_colim_enriched_map_in (w : C) (gs : ∏ (i : I), D i --> w) (qs : ∏ (i j : I) (f : i --> j), # D f · gs j = gs i) (i : I) : enriched_conical_colim_cocone_in a i · is_conical_colim_enriched_arrow w gs qs = gs i.
proof: Proof. unfold is_conical_colim_enriched_arrow, enriched_conical_colim_cocone_in. use (invmaponpathsweq (make_weq _ (isweq_enriched_from_arr E _ _))) ; cbn. rewrite enriched_from_arr_comp. rewrite !enriched_from_to_arr. rewrite tensor_split'. rewrite !assoc. rewrite mon_linvunitor_I_mon_rinvunitor_I. rewrite <- tensor_rinvunitor. etrans. { rewrite !assoc'. rewrite !(maponpaths (λ z, _ · z) (assoc _ _ _)). apply (limArrowCommutes (make_LimCone _ _ _ (pr2 a w))). } cbn. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.OppositeCategory.Core UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoproducts UniMath.CategoryTheory.EnrichedCats.Colimits.EnrichedCoequalizers