Lemma cat_of_elems_on_nat_trans_is_functor (α : X ⟹ Y) : is_functor (cat_of_elems_on_nat_trans_data α). Proof. split. - now intros a; apply cat_of_elems_mor_eq. - now intros a b c f g; apply cat_of_elems_mor_eq. Qed.
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.