proposition: Lemma yoneda_iso_sets (C : category) (c : C) (F : functor C^op HSET) : is_z_isomorphism (C:=HSET) (a := make_hSet (hom _ ((yoneda C) c) F) (isaset_nat_trans_yoneda C c F)) (b := F c) (yoneda_map_1 C c F).
proof: Proof. set (T:=yoneda_map_2 C c F). simpl in T. set (T':= T : hom HSET (F c) (make_hSet (hom _ ((yoneda C) c) F) (isaset_nat_trans_yoneda C c F))). exists T'. split; simpl. - apply funextsec; intro alpha. unf; simpl. apply (yoneda_map_1_2 C c F). - apply funextsec; intro x. unf; rewrite (functor_id F). apply idpath. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.whiskering