proposition: Lemma forms_equivalence_disc_fib : forms_equivalence adjunction_data_disc_fib.
proof: Proof. split. - intro F. apply nat_trafo_z_iso_if_pointwise_z_iso. intro c. cbn. set (XR := hset_equiv_is_z_iso _ _ (idweq (pr1 F c : hSet) )). apply XR. - intro F. use (_ ,, (_,,_ )). + apply ε_inv_disc_fib. + apply eq_discrete_fib_mor. intros. apply idpath. + apply eq_discrete_fib_mor. intros. apply idpath. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Examples.Opposite