Theorem Representation_to_z_iso {C:category} (X:[C^op,HSET]) (r:Representation X) : z_iso (Hom1 (universalObject r)) X. Proof. refine (z_iso_from_nat_z_iso _ ((element_to_nattrans X (universalObject r) (universalElement r)),,_)). intro b. apply (pr2 (weq_iff_z_iso_SET _)). exact (pr2 (pr2 r) b). Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import Require Import Require Import UniMath.MoreFoundations.Tactics.