proposition: 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: Proof. exact (maponpaths (make_ob I) (eqtohomot (functor_id X I) ρ)). Defined.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf