proposition: Proposition enriched_conical_colim_from_coprod_coequalizers_commute (i : I) : enriched_conical_colim_from_coprod_coequalizers_mor · precomp_arr E w (enriched_conical_colim_in_from_coprod_coequalizers i) = fs i.
proof: Proof. unfold enriched_conical_colim_from_coprod_coequalizers_mor. unfold enriched_conical_colim_in_from_coprod_coequalizers. rewrite precomp_arr_comp. rewrite !assoc. rewrite (EqualizerCommutes (is_coequalizer_enriched_to_Equalizer E f g enriched_conical_colim_ob_from_coprod_coequalizers_is_coequalizer w)). rewrite (ProductPrCommutes _ _ _ (is_coprod_enriched_to_Product E D is_coprod_tar w)). 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