proposition: Lemma functor_from_equivalence_is_essentially_surjective : essentially_surjective F.
proof: Proof. unfold essentially_surjective. intros b; apply hinhpr. exists (G b). apply counit_pointwise_z_iso_from_adj_equivalence. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core