Lemma make_ob_identity_eq {I : C} (ρ : pr1 (pr1 X I)) : make_ob I (# (pr1 X) (identity I) ρ) = make_ob I ρ. Proof. exact (maponpaths (make_ob I) (eqtohomot (functor_id X I) ρ)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf.