Lemma exp_functor_is_functor : is_functor exp_functor_data. Proof. use make_dirprod. - intro; reflexivity. - intros ? ? ? ? ?; reflexivity. Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Categories.Type.Core. Require Import UniMath.CategoryTheory.Categories.Type.Limits.