proposition: Theorem subobject_classifier_balanced : (is_z_isomorphism f).
proof: Proof. assert (p : f = EqualizerArrow (f_asEqualizer)). { apply idpath. } rewrite p. use (z_iso_Equalizer_of_same_map f_asEqualizer). exact path_from_fepi. Defined.
imports: UniMath.Foundations.PartA UniMath.Foundations.PartB UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Subobjects UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Core.Functors UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Subcategory.Core