Definition makeRepresentation {C:category} {c:C} {X:[C^op,HSET]} (x:c ⇒ X) : (∏ (c':C), UniqueConstruction (λ f : c' --> c, x ⟲ f)) -> Representation X. Proof. intros bij. exists c. exists x. intros c'. apply set_bijection_to_weq. - exact (bij c'). - apply setproperty. 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.