proposition: Lemma iso_between_coequalizer_enriched_inv {a b : enriched_coequalizer_cocone} (Ha : is_coequalizer_enriched a) (Hb : is_coequalizer_enriched b) : map_between_coequalizer_enriched Ha Hb · map_between_coequalizer_enriched Hb Ha = identity _.
proof: Proof. unfold map_between_coequalizer_enriched. use (underlying_Coequalizer_arr_eq Ha). rewrite !assoc. rewrite !underlying_Coequalizer_arr_in. rewrite id_right. 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.Monoidal.Categories UniMath.CategoryTheory.EnrichedCats.Enrichment UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers