proposition: Lemma isEpi_pw_pr_quot_functor : ∏ x, isEpi (pr_quot_functor x).
proof: Proof. intros a z f g eqfg. apply funextfun. intro x. eapply surjectionisepitosets. apply issurjsetquotpr. apply setproperty. intro u. apply toforallpaths in eqfg. apply eqfg. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Epis UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.EpiFacts UniMath.CategoryTheory.Limits.Coequalizers