proposition: Lemma isaprop_split_essentially_surjective (A B : category) (HA : is_univalent A) (F : functor A B) (HF : fully_faithful F) : isaprop (split_essentially_surjective F).
proof: Proof. apply impred; intro. now apply isaprop_sigma_z_iso. 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.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core