proposition: Lemma weq_to_iso_SET {X Y:HSET} : z_iso X Y ≃ ((X:hSet) ≃ (Y:hSet)).
proof: Proof. intros. apply weqfibtototal; intro f. apply weqiff. - apply weq_iff_z_iso_SET. - apply isaprop_is_z_isomorphism. - apply isapropisweq. Defined.
imports: UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.Foundations.Preamble UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics