proposition: Lemma ff_essentially_surjective_to_split (A B : category) (HA : is_univalent A) (F : functor A B) (HF : fully_faithful F) (HF' : essentially_surjective F) : split_essentially_surjective F.
proof: Proof. intro b. apply (squash_to_prop (HF' b)). - apply isaprop_sigma_z_iso; assumption. - exact (idfun _). Defined.
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