proposition: Proposition underlying_Coequalizer_arr_eq {w : C} {h₁ h₂ : a --> w} (q : enriched_coequalizer_cocone_in a · h₁ = enriched_coequalizer_cocone_in a · h₂) : h₁ = h₂.
proof: Proof. refine (!(enriched_to_from_arr E _) @ _ @ enriched_to_from_arr E _). apply maponpaths. use (EqualizerInsEq (is_coequalizer_enriched_to_Equalizer Ha w)). cbn. unfold precomp_arr. rewrite !assoc. rewrite !tensor_rinvunitor. rewrite !assoc'. rewrite !(maponpaths (λ z, _ · z) (assoc _ _ _)). rewrite <- !tensor_split'. use (invmaponpathsweq (make_weq _ (isweq_enriched_to_arr E _ _))) ; cbn. rewrite !assoc. rewrite mon_rinvunitor_I_mon_linvunitor_I. rewrite <- !(enriched_to_arr_comp E). exact q. 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