Lemma uOF_identity {C:category} {X:[C^op,HSET]} (r:Representation X) : r \\ (identity X ⟳ r) = identity _. Proof. unfold nat_trans_id; simpl. unshelve refine (transportb (λ k, _ \\ k = _) (identityFunction' _ _) _). apply universalMapIdentity. Qed.
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.